The Two-Face storyline Reprinted in Limited Collector's Edition #C-37
IIRC the Two-Face of the comic strip actually appeared before the Two-Face of the comic books. So it's interesting to see what they kept & what they didn't.

This Two-Face is Harvey Apollo, a vain actor, which makes his theatricality a lot more believable than District Attorney Harvey Dent. (Although the second comic book Two-Face was also an actor.)

In the first strip (these seem to be Sunday pages) Harvey's left hand is flesh colored after the accident, but from the second strip on it's green.

Why does Harvey have the two-headed silver dollar? Did the DA give it to him after the trial?

Okaaaaaaaaaaaaay, the seventh strip has Batman & Robin in a windowless room. Two-Face is going to toss in two cyanide capsules. To make Two-Face think it had worked they tie their capes together to catch the capsules & smash their watches against the wall to make him think the capsules have broken. My problem is the artist drew the capes as if B&R are holding them with both hands, but they're only holding the capes one-handed. Now maybe B&R somehow attached the capes to their utility belts on that side, but I still think it's badly drawn.

All strips reprinted in Batman: The Dailies 1943-1946

The cover shows Two-Face, Joker, Catwoman & Penguin, but only Joker appeared in the daily strips.

What A Sweet Racket!
Strip 38. December 14, 1943. Spike Durphy says that his gang paid Blackie to spring him from jail
Thing is Spike escaped from prison by hiding in Commissioner Gordon's car. How did Blackie's people arrange that?

The Phantom Terrorist
Strip 120. March 18, 1944. Dick says, "I'm glad they let Rita Rollins go for turning state's evidence. She really wasn't bad".
Really? A year earlier she testified that John Corliss had stolen money from Claude Towne when she knew Towne had stolen money from Corliss.
Let's see, Conspiracy, False witness, Perjury, at least.
Then she blackmailed Towne into saying she was the star of a show & the real star was forced to pretend to be Rita on stage & this caused Towne to try & destroy the show pretending to be a phantom of the opera type character.
I'd say she was plenty bad & deserved to spend time in the joint.

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NNAN, but it seems like poor planning. They have a story where Batman doesn't even appear (because for most of it Bruce Wayne is handcuffed to another person) & they follow it up with a silly story where Batman has to find an apartment for the daughter of a guy who gave the Police fund $100,000. Not that either story was bad, but after a story without seeing Batman & Robin in costume you'd think they would want to do a story that shows Batman & Robin punching out some serious bad guys, not something light & trivial.

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The Warning Of The Lamp
Strip 635. November 8, 1945. The Lamp says he wants to buy Gribbidge's ranch & "destroy the cattle".
He's been preaching a vegetarian philosophy. How does killing cattle match the vegetarian philosophy?

A History Of The 1940s Batman Newspaper Strip Part 3
Page 8 (since the book was originally three different books they kept the numbering of the original volumes).
Talking about the car shortages of, & after, WWII he wraps up with this sentence, "Pent-up demand far exceeded post-war supplies, which is why even millionaire Bruce Wayne had to look for a used car in this story."
Actually it's explained in the story that Bruce was working with the DA to get evidence on a hot-car ring.

Page 13.
"known as the Blue Network when the shown premiered".
Show, not shown.

An Affair Of Death
Strip 678. December 28, 1945.
The headline of the Gotham Gazette adjusts its margins. Panel 1, we can read the headline despite the fact that Batman's face should cover some of it, but in Panel 2 the lines of the headline is now left justified.

Strips 686-689. January 7- 10, 1946. Batman & Robin have set up a trap to catch some crooks. They get the gypsy kid the crooks had kidnapped & he says that they had come on Route 64, just three miles beyond the hill. Batman races out to see if he can catch them. Robin then decides to disguise himself as the gypsy & put himself up as bait. Batman returns to the cabin & finds out what Robin had done, the next strip shows Robin back in Gotham.
Did Robin run the whole way or did he take the Batmobile & let Batman & the gypsy walk?

Strips 698-704. January 21-28, 1946. Someone should have taught Bob Kane how to draw people tied up. Robin & Juanita are tied to a car lift & the ropes go around the necks & waists & their hands are inside the waist ropes.
1. The rope around Robin's neck looks so loose that Robin should be able to get his head under it.
2. Their hands are not individually tied, they're just inside the ropes. There is no reason why they can't slip their hands out from there.

A Change Of Costume
Strip 723. February 19, 1946. A thug refers to Batman & Robin as "It's them bums from Brooklyn!"
Gotham City has a Brooklyn area?

The News That Makes The News
Strip 753. March 26, 1946. The idea that Gotham was, apparently, its own state didn't originate in the 1970s as this strip features "Rae Raleigh, woman senator from Gotham" & 4 days later we see her office in Washington, DC.

Strip 760. April 3, 1946. Earlier Batman & Robin 'unofficially detained' Edgar Poole until the Senate could gather the evidence to have him arrested. In this strip a disguised Batman shows Senator Raleigh a police department badge* identifying him as Batman.
Okay, you're either a policeman or you're not, you can't play it both ways.

* It's a bat-shaped badge reading "Batman P.D." so apparently Batman is his own police department. ;-)

Ten Days To Live!
Strip 852. July 19, 1946. In strip 836 Robin refers to the mysterious fat man as Mr. Fat. All well & good since they don't know his real name, however in this strip Mike Wren refers to the fat man as Mr. Fat indicating that that is a name he goes by.
Holy good guessing, Robin!

Acquitted By Iceberg
Strip 905. September 20, 1946. Panel 2, Iceberg is trying to stab Batman, but the watch dog Lucifer attacks Bats by leaping on his back & gets stabbed with the knife, the cut leash is sticking out behind the dog at about the Iceberg's shoulder level. Panel 3 the dog runs off the cliff with its leash wrapped around the Iceberg's ankle.
Wha...?
Had the leash wrapped around the Iceberg's wrist that might have made sense since it was near the leash, but his ankle???

Deadly Professor Radium
When nitpicking the comic strips I just assumed the comics had a separate continuity from the comic books (Earth-2b instead of Earth-2) & a story like this (a rewrite of a story from Batman #8) didn't happen before since Batman & Robin never mentioned the earlier Professor Radium.

Strip 921. October 9, 1946. The quote marks around "merciful death" in the policeman's speech indicates that it's a quote from Professor Radium's note, but the actual note said "merciful release".

All strips reprinted in Batman: The Sunday Classics 1943-1946
The Secret of Cap'n Plankton's Ghost
Strip 10. January 9, 1944. Batman smashes through a window & the broken glass cuts the rope his hands are bound with..., but nothing else.

Cap'n Alfred
Strip 28. May 14, 1944. Opening caption contains the line, "a fleet of silk trucks is hijacked".
'Are hijacked' sounds better, but I'm not sure if it's incorrect. I assume the author used "is" because of the word "fleet".

A English Society Skoit
Strip 69. February 25, 1945. NANJAO. In the books Alfred only became a butler because he'd promised his father on his deathbed that he would follow the family business & became the Wayne's butler. In the strips Alfred Beagle had been a butler in England before becoming the Wayne's butler. Different continuities.

However, as I understand it, what we in the states call a butler is actually called a valet in England. In England a butler deals with bottles IIRC.

Strip 70. March 4, 1945. Batman asks, "Dick, why should a girl fresh from England say dough instead of money".
Because it's Cockney rhyming slang. "Money" becomes "honey & dough", which gets shortened to "dough".

The Gopher: King Of The Underworld
Strip 83. June 3, 1945. Here we find out that the Gopher's face was just a mask. One of them magical masks that pops up in comics so it seems to be a real face.

The Tale of The Tinker Diamond
Strip 86. June 24, 1946. Diamond cutter, Mr. Brock, explains to Batman, "Each diamond is grained like wood! Unless the cleaving tools strike just so, the stone can shatter into many chips!"
As I understand it, by the time you get to the cleaving point the stone has already had a small cut made along the cleavage plane and it's only if that's been screwed up will the diamond shatter.

A Pretty Amnesiac
Strip 93. August 12, 1945. In the Russian quarter of Gotham, Robin finds himself unable to drink the tea because the glass is too hot, but the amnesiac shows him the correct way to hold the glass.
Why do I consider this a nit? Because the amnesiac is bare-handed, while Robin is wearing gloves.
Possible Anti-nit. Robin is a wimp. ;-)

Strip 94. August 19, 1945. Robin says, "They'll be in their jalopy and away before we can reach them."
Batman adds, "And the Batmobile won't be able to chase them through these crowded streets!"
Crowded? The artist only drew 3 kids in the street.
And if it's so crowded how can the jalopy make a getaway? Wouldn't the crowd hinder them as well?
A better explanation would have been that the Batmobile had been left too far back & the jalopy would have been out of sight by the time they got to it.

Strip 95. August 26, 1945. I've never seen Bocci balls as big as these. They almost look like bowling balls.

Devil's Reef
Strip 99. September 23, 1945. Alfred has rowed a boat to Devil's Reef, apparently with no problem other than navigational. However during the Cap'n Alfred storyline (June 4, 1944 in particular) Alfred got seasick when he took the ferry boat into the sea.
Admittedly it might have specifically just been the "rough sea" in that earlier story & that this time the water was smooth enough, but I thought I'd mention it.

Strip 103. October 21, 1945. Alfred came to Devil's Reef to find a treasure marked on a treasure map. To free Alfred & Robin from a cave, Batman alters the map so crooks think the treasure is in the cave. Alfred donates the map to a museum (the treasure was long gone) and the museum says the map is "the treasure of their cartographic collection."
Makes one wonder how bad the other maps are if a vandalized map is the best?

Gotham's Cleverest Criminal
Strip 104. October 28, 1945. For some reason the Joker is wearing a purple outfit instead of the b&w striped outfits of the other prisoners.

Strip 106. November 11, 1945. Joker's face is flesh-colored instead of white.

Strip 107. November 18, 1945. Where did Batman get the anti-tank 'blocks' & how exactly did he set them up? If they're heavy enough to stop tanks (& they did stop a runaway truck without budging) it would take more than just pluck & a teenage boy to set them up.

The Sparrow's car is ridiculously small. I suppose they had to draw it small to 'believably' get between the space between the anti-tank blocks, but it does not look big enough for two people to sit in.

NNAN but certainly an unusual artistic license. In the final panel the Joker is drawn tiny as he finds out he has been saved by the criminal mastermind he wanted to beat (to emphasize how small he feels, I believe), but it really seems out of place since the artists usually use a more realistic style.

Twelvetoes
Strip 115. January 13, 1946. In the previous strip the statue was colored mostly brown which made it look like bronze, but here it's white & blue like it's supposed to be marble.

Tire Tread Deathtrap
Strip 156. October 27, 1946. The Batmobile is purple instead of blue.

Me - IIRC the Two-Face of the comic strip actually appeared before the Two-Face of the comic books.
I was wrong.

Their Toughest Assignment Strips 530-577. July 9 - September 1, 1945.
I thought about this while reading it, but forgot to write it down. Batman & Robin are trying to find an apartment for the daughter of a man who donated a lot of money to the police emergency fund, however there is a housing shortage in Gotham City. Bruce Wayne is a millionaire, why doesn't he buy some land and have some apartment buildings built? (True it wouldn't be finished in the time they need to find an apartment, but still it would be a way to deal with a big problem that the city is facing.)