Abusive Parents: Frank's parents are actually very supportive of their son, but his father engages in emotional abuse in one of his last scenes. Frank has been trying to stop his criminal lifestyle for a while now, but can't go through with it until his father tell him that it's alright to do so. Instead Frank Sr. refuses and tries to use his son as a weapon against the government because they didn't support him when his business went under. Note that this did not happen in real life; see Very Loosely Based on a True Story below.
Beat Them at Their Own Game: Frank's in a hotel room wearing James Bond's suit, making out with a model when she gets up and negotiates him up to $1000 for the night. Frank's about to walk downstairs to cash a check ... and ends up signing a $1400 check over to her in return for the $400 difference.
Brick Joke: After Hanratty's boss chews him out and clearly gets on Hanratty's nerves, Hanratty references his previous Precision F-Strike by going "Chief? Knock Knock."
From that same pair of scenes, Carl tells his fellow agents that if they just keep their eyes open and do their jobs, he'll buy them both a Good Humor bar, though at the time it seems like a throwaway condescending line. Guess what those two agents are munching on back at the boss' office?
Criminal Mind Games: Played with, as Frank calls Hanratty yearly at Christmas; not to taunt him, but because of crushing loneliness.
Cut Lex Luthor a Check: Frank eventually gave up the life of crime and discovered he could make more money as a fraud consultant.
Dawson Casting: Frank ages from 16 to his early twenties over the course of the film; he was played by a 27-year-old Leonardo DiCaprio. Justified in that the real Frank Abagnale looked older than his age, which was how he got away with many of his scams. And that's invoked in-movie; Hanratty's initial profiling of Abagnale after their first encounter includes being age 26 — 30.
Distracted by the Sexy: How Frank gave the entire FBI the slip at Miami Airport. Just get in the middle of a group of (wannabe) stewardesses, and you're invisible!
Freudian Excuse: Frank comes from a broken home and he ran away since he couldn't deal with choosing one parent over the other.
Averted in the book. Abagnale says he had a hard time when his parents divorced, but he also says more than once that it's no excuse for his crimes, and most other children from "broken homes" don't become con artists.
Friendly Enemy: Frank Abagnale Jr. and Carl Hanratty. It's done in an interesting way early on. Frank calls Carl to apologize for the fact that Carl has to deal with his crimes. He's being totally sincere, but Carl just thinks he's mocking him. It's one of the many things in the movie that show that while Frank may be a criminal mastermind, he's ultimately just a kid.
One Dialogue, Two Conversations: When Frank asks Brenda's father for permission to marry her. When Frank says that he isn't a doctor or lawyer but just a kid in love with his daughter, Brenda's father thinks Frank's only being sentimental.
It should also be noted that something Frank learned from his father plays into this as a bit of a Running Gag. "Why do the Yankees always win?" "Because the other teams are too busy looking at the damn pinstripes."
Sherlock Scan: A non-visual example in Hanratty being able to discern clues of Frank's whereabouts from his telephone calls; e.g. he figures out Frank's from New York from his mention of the Yankees, and that he's a kid from his use of the alias Barry Allen.
Frank himself demonstrates a highly acute attention to detail throughout the film, starting with informing a classmate that her fake "note from mother" is missing a crease to be believable.
Shout Out: The dollar floating under the door and fluttering like a feather past Tom Hanks is a nod to Forrest Gump.
Squick: In-Universe: When "Dr" Frank sees the young boy with a broken leg, bleeding, and moaning in pain, he is very squicked and has to hold it in until he gets the other doctors to diagnose the treatment before bolting out to throw-up.
Star-Making Role: Oddly averted for Amy Adams, who despite being prominently featured as Frank's girlfriend had to wait until Enchanted some years later to become an A-lister.
And Spielberg actually cast her in order to make that star, and said he was crushed when her career didn't take off immediately. But her career got better, so it all worked out in the end.
To Tell the Truth: The real Frank Abagnale, Jr. appeared on an episode of this show. The movie is framed by actual episode footage of this appearence with DiCaprio digitally inserted into Abagnale's place.
Very Loosely Based on a True Story: Besides throwing in the Freudian Excuse for Frank becoming a con-artist and counterfeiter, many details from Frank Abagnale Jr.'s life were altered or added in the film. For instance, Frank is shown as an only child, when in real life he had three other siblings. But most notably, he is depicted reaching out to his father in-between cons, whereas the actual Frank never saw or spoke to his father again after leaving home. This drastically changes Frank's motivation in the film: his relationship with his father is portrayed as having been so close that he can only stop his criminal lifestyle if his father wants him to; instead his father (still embittered over the lack of support he received when his business went under) refuses and uses his son as a weapon to get back at the government. In reality no such thing happened of course - Frank continued simply because he was good at it, and because it was preferable to getting a hard-working job or going to jail.
Frank's quasi-friendship with Carl while Frank is on the run is entirely invented, although Frank and the agent who was chasing him did become friends after Frank was released from prison.
He certainly didn't escape from the plane they way they show it in the film. For one thing the septic tank on aeroplanes rarely detours into the luggage area.
In his memoir Frank claims to have done exactly that (escaped out an aeroplane toilet). Of course, his memoir was Very Loosely Based on a True Story as well. In the memoir, he had flown back to the United States on a Vickers VC10; the toilet unit lifts out, so he could have escaped.
Frank was not finally caught in France by any cunning FBI work. What actually happened was that after he had gone to ground in a small village, he was spotted by a Pan Am stewardess on vacation, who notified the police.
Also they missed out the bit after his release from the appalling French jail when he spend a year in a Swedish jail. And that it was his Swedish lawyers who helped him become repatriated to the US (to jail) so he wouldn't have to serve 5 years in jail in each European country.
Villain Protagonist: Frank Abagnale Jr., the protagonist, is an adrift and young counterfeiter and con man who uses his natural cleverness to make some money, and his antagonist, Hanratty, is an FBI agent trying to, well, Catch Him if He Can. In the end Frank with Hanratty's support eventually goes straight.