Can someone please explain the relevance of the game show at the start with three guys saying they were Frank Abergnale? Did this game show really happen?

There was a game show in the '60's (I believe it was revived in the '80's or '90's) called To Tell the Truth. The producers would find someone with an interesting history and bring him/her and two imposters on the show. The host would read the real contestant's statement to the celebrity panel, who would then attempt to ferret out the real "John Smith" (or Frank Abergnale, etc.) by asking the three contestants pointed questions

Did Frank Abergnale really appear on such a show?

It's certainly possible, but there's mention of it on the page for Abagnale at the Internet Movie Database. The only listing for any work he's done was as one of the French gendarmes who arrest Frank (DiCaprio) toward the end of the movie.

From what I read, John Williams composed the soundtrack for this movie. It's been nominated for an Oscar. (That's 42 nominations now!)

Yes, he did appear on To Tell the Truth, but he appeared to be much older than how Leo looks in the film at the time.

I think I read that they used much of the same footage as well (with some computerized changes).

I loved this film. DiCaprio's best acting job that I've seen and Walken is amazing too. Their last scene is heartbreaking ("Where ya going, Frank? Where ya going?"). The only problem is that the film is a little too long and sort of obvious at the end. The film should have been a breezy comedy/drama, not an "epic."

This really is a great film, although the part with Jennifer Garner seemed pretty pointless to me. Fantastic acting, beautiful look and feel to the movie, and the little touches really add something.

The TTTT footage used in the film was from the original show, but DiCaprio was Gumped into the footage. (Better technology these days, I couldn't even tell.)

I don't consider this an "epic," but a nice, breezy entertainment. Excellent and atypical score from John Williams, reminiscent of a lot of '60's Henry Mancini scores. Leo is actually a lot of fun to watch.
To Tell The Truth has had many incarnations over the decades (six, according to IMDB.) The footage used in the film is taken from the second incarnation of the game.
In the scene where Frank Abegnale Sr. (Christopher Walken) is going to the bank, there is a Duane Reade drug store in the background. The logo on the store is the current one, not the one from the 1960's.

Also, Frank Jr. drives a 1965 Chevelle 2-door hardtop to pick up his "wife" at Miami Airport. However, the wiper blades on the Chevelle are the aerodynamic type with holes in them. They weren't available until the late '80's, or early '90's.

There's one scene, apparently for comic effect, where we see Handratty (Tom Hanks) at a laundromat washing his shirts. He takes his shirts out of the machine, and they've turned from white to pink. The previous user of the machine carelessly left a red garment in it, which bled all over his white shirts. The problem is, the shirts look too evenly colored pink to have been bled on; they look like pink shirts wet down. I don't think the red garment would have bled so evenly over the shirts.

When the three FBI agents come to visit Frank's mom (Nathalie Blye), she serves them Sara Lee cake. One of the agents comments "Nobody doesn't like Sara Lee". Correct me if I'm wrong, but I don't think Sara Lee used that tag line until at the earliest, the mid-1970's.

I also interpret this movie as yet another way that Spielberg deals with his parents' divorce, as Frank's parents divorce early in the film. (ET is also interpreted as Spielberg's working through their divorce.) Come on, man. Spielberg was 55 years old when he made this picture, and he has apparently still had yet to come to terms with it. Even though he had his own mega-divorce from Amy Irving.

This was the movie that changed my opinion of DiCaprio. I had a very strong irrational bias against him because of the teen heartthrob thing from Titanic, which wasn't his fault.

But he really shows his acting chops in this movie.

Another anachronism in this film is - in scenes set in the late 1960's (such as the airport scene with the aforementioned Chevelle) we see Checker brand cabs with 1970's style crash bumpers. (Checker stopped building cars in 1982)
I was in an Office Depot (they're going out of business) and the store had Uniball pens for sale, with what looked like the "Frank Abagnale Seal of Approval." I don't know if that constitutes an endorsement, but it seems pretty close.

When we see the pilot and flight attendants (we don't call them "stewardesses", do we?) get out of a car, the "Walk/Don't Walk" sign in the background is the flashing hand one used now, not the steady green "Walk"/flashing "Don't Walk" signs used in the 1960's.
When Frank applies an airplane model's "Pan-Am" decal to a check to forge a Pan-Am payroll check, he puts the decal on the check slightly crooked. And, gives it to the bank teller that way.

In a move I consider ill-conceived and totally asinine, a musical play based on this movie is headed to Broadway, scheduled to open Spring 2011. More here.

Fun movie. Not too sure about the accuracy, but a good story none the less.

Regarding accuracy, some parts are verifiably true. The real Frank Abagnale did steal millions by passing bad checks in the era before electronic verification. He also passed the bar in Louisiana despite never having attended law school; in the way depicted in the film. Basically you could take the test as many times as you wanted (and it was always the same) so all he had to do was figure out which questions he didn't know the answer to and look them up for next time.

Ever since Abagnale started speaking about his exploits in 1970s people have been questioning the accuracy of some of his claims. His escape at the airport where he removes an airplane toilet and gets out of a plane on the runway couldn't happen, per airplane mechanics. Similarly nobody can verify his stories about posing as a doctor in a Georgia hospital. He hand waves it away by saying "well they wouldn't want to admit to that, now would they." Which may or may not be accurate. The best commentary I've heard on the whole issue was somebody who said "so a con man writes a book about his life and people are shocked that he exaggerated and made some of it up?"

This really is a great film, although the part with Jennifer Garner seemed pretty pointless to me.

The ultimate point of that scene is that Frank actually pays her with a bad check and actually get's cash back from her. So she actually paid him several hundred dollars to spend the night with him when she was trying to sell her services, sexually speaking, to him.

Near the end of the film, after Carl catches Frank printing money in France, the French police show up and arrest Frank. The white-haired older policeman in charge of his arrest is the real life Frank Abagnale.

Here's an interview with Frank Abagnale, from the New York Post. Which was done in conjunction with the musical version of the film opening on Broadway. BTW, the play is getting less-than-stellar reviews.
How did Frank pay for all those Pan-Am airplane models, from which he soaked the decals off to make his fake payroll checks? May we assume he paid by check?

We see modular phones being used during the film, which for the most part is set in the 1960's. Modular phones didn't come into use until 1976.