The trial of Eureka the kitten near the end of this book not only reveals several differences between the Ozian justice system and that of the U.S., but ultimately is made highly unbelievable by several odd features. First of all, there is apparently no requirement that one be a resident of Oz to sit on a jury, since the jury includes Zeb and Jim the cab-horse. This is not that strange, since, after all, Eureka herself is not a resident. However, there is also apparently no rule against having jurors who know the accused, since Zeb and Jim have shared a long, dangerous journey with Eureka, which might well prejudice them for or against her (more likely against her, under the circumstances). Finally, when the actual truth about the piglet's disappearance is revealed at the end of the trial it becomes evident that while Eureka is innocent of murder she is guilty of what would probably be termed "assault with intent to murder" in the U.S. Yet Eureka receives no punishment from the court whatsoever. Baum does go on to say that Eureka was subsequently ostracized in the Emerald City because everyone knew she had wanted to eat the piglet, and that this contributed to Dorothy's decision to return to Kansas with her soon afterwards, but in my opinion Eureka should have received some actual punishment, such as being forced by Ozma to return to Kansas immediately, or even being imprisoned in the Emerald City for some further amount of time.

Not to mention the utter lack of anyone trained in logical legal thinking!

Anyways...
At the beginning of this book Eureka is described as pink because she is a white cat sitting in the light of a pink sun. All well and fair. Why is she still pink 10 books from now? Did she fall into a vat of beets sometime early in her permanent Ozite stay?

The deuz ex machina at the climax of this adventure is quite disappointing. If Dorothy knew all along that Ozma would be looking in on her at the end of the week, why didn't the travellers just stay on with their hosts in the Valley Of Voe (eat the damas and take a role call before leaving!) and relax in comfort until they could be rescued? Why bother fighting the Gargoyles and Dragonettes?

How does one send an electro-physical signal to "flap" a wing that is attached to a buggy but not to one's person?

According to this book, there are no real horses in Oz. Yet two books ago, Tip, a native Ozite from birth, described the differences between a "real horse" and a "sawhorse" quite accurately.

In books 3-5, it takes Dorothy quite a while to remember that while she is enjoying princessly delights in the lap of luxury, her aunt and uncle are in grief over her supposed death. Specifically, why is it only the kitten who wants to go home so badly?

The "history of Oz" which Ozma gives the Wizard over dinner does not bear up under scrutiny, particularly when one notes that Ozma is Tip and was present two books ago when Glinda recounted the Wizard's theft of the throne from her father. So far we now have three separate accounts of early Ozite history:
1) In book 1, the Wizard merely remarks that "the people" made him their ruler and he oversaw the construction of the Emerald City. This can be discounted as the Wizard was probably omitting facts to make himself sound like a benevolent despot.
2) In book 2, Glinda notes that the Wizard took the throne from King Pastoria and had the unscrupulous witch Mombi enchant baby princess Ozma so she could not be produced as a true heir.
3) Now, Ozma says that Mombi kidnapped the her grandfather, jailed both him and her father (very kind of the witch to let her captive marry and produce two more generations of heirs...!), and then enchanted her. She also says that all male rulers of Oz were named Oz (King Pastoria Oz?).
I think Ozma is really confused, and given her presence in book 2, she has no excuse.

The people of Oz sure give the Wizard a warm welcome considering he was a con artist and humbug who took the throne from the former king and organized (...enslaved?) the citizens into his own private construction crew.

I notice the Wizard isn't scolding Dorothy, the Scarecrow, the Tin Woodsman, or the Cowardly Lion for blabbing his secret to the entire world.

I think that's all for now.

If Mombi had indeed kidnapped Ozma's father and grandfather before the Wizard's arrival, and the Wizard subsequently took the baby Ozma to Mombi clandestinely, the people of the Emerald City might not realize that the Wizard had anything to do with the fall of the rightful regime. Also, perhaps the people enjoyed building the Emerald City; they certainly enjoy living in it now that it exists, and in the next book, "Road," Baum has the characters talk about how much the Oz people enjoy their work.
Obviously, Ozma knows the information about the Wizard's past and her own revealed in "Land," but since she can surely tell that the Wizard is a good person at heart she presumably would not want to embarrass him by reminding him and everyone else of his role in her captivity. In Ruth Plumly Thomson's "The Lost King of Oz," the Wizard is presented as feeling intense remorse over his role in Ozma's imprisonment by Mombi as described in "Land."

Personally, I decided that Ozma deliberately told a different story here to lessen the Wizard's role in her disappearance.

I don't think the version of the story in which Mombi was also the jailer of Ozma's grandfather has been used again in later books. But I could be wrong. Most histories of Oz go with the story that Ozma's father, King Pastoria, was the ruler of Oz until he (and Ozma) disappeared, and the Wizard took over.

As for the 'deus ex machina', I agree that it is disappointing, after seeing Dorothy, the Wizard, and friends escape the Mangaboos, the Invisible Bears, and the Wooden Gargoyles on their own. All I can conclude is that Baum was making it up as he went along, and he needed some way to get the travellers to Oz. Dorothy's mention of her 'signal to Ozma', when it comes, is sort of a big 'by the way'.

Of course, it's said Dorothy could have used the magic slippers to return to Kansas at the very start of 'The Wizard of Oz', but if she did, the Scarecrow would still be on his beanpole, the Tin Man would still be rusting in the forest, and the Lion would be too ashamed to be seen among the other animals. And of course, the Wicked Witch of the West would still be around to torment the Winkies.

Here, however, Dorothy and company don't do very many heroic acts aside from saving themselves, before finally giving up and signalling Ozma to get them out of a dead-end cave. So it's not as if they saved the world or anything because they DIDN'T wait around in the Valley of Voe (or some other safe place) instead of facing the later dangers...