Corpsing: As Harry and George reunite after being apart for so long, there's a noticeable ear-to-ear grin on the baggage porter.
Possibly justified in that it's a small town so he may know them and recognize the significance of the moment.
Dawson Casting: 38-year old James Stewart and 25-year-old Donna Reed trying to pass as teenagers. Justified in that they need to play older versions of their characters as well.
In a bit of Lampshade Hanging, Uncle Billy notes that "Nobody changes, here!" after Harry comes home from college.
Doing It for the Art: During filming of the scene at Martini's Bar, James Stewart was so overcome with emotion while praying that he began to shed manly tears for real. Seeing this, Capra had to reframe the shot in order to get it closer than was actually filmed because he wanted to catch the expression on Stewart's face. At the time this was an extremely time-consuming project, each frame had to be done individually, making it only one step away from stop-motion animation. Capra spent the whole night doing it.
Remember, too, that at one point Stewart had wanted to leave Hollywood behind after his World War II experiences. That Capra was able to woo him back into acting is this all over.
Irony as She Is Cast: George Bailey is denied from military service during World War II because of his deaf left ear. His little brother is accepted and becomes a medal winning pilot. The real Stewart was a bomber pilot and Lt. Colonel in WWII, later being promoted to Brigadier General after the war.
Uncle Billy staggers away drunk from a party, you hear a crashing metal sound, and (offscreen) he calls back "I'm all right! I'm alllllllll right!". We presume that Uncle Billy stumbled into some garbage cans. In fact, the crashing noise was from a stagehand dropping equipment, and Thomas Mitchell's "I'm all right!" was an ad-lib. The stagehand got a bonus.
The first kiss with Mary, Jimmy Stewart was nervous about his first onscreen kiss since coming back from World War II. It was filmed in one unrehearsed take and part of the kiss had to be cut due to being too passionate for the censors.
From the same scene, there were more lines that George was going to say to Mary before kissing her, but Stewart essentially pulled a "Shut Up" Kisson himself and just cut ahead to the act of passion.
In the scene when there's a run on the Savings & Loan, Ellen Corby (in her only scene in the film) threw in her request for a very specific amount of money, not just her entire savings back; Stewart was so amused that his reaction is genuine.
Vindicated by Cable: It was not a big hit on initial release. It actually became a public domain title in 1974, so virtually every TV station around started airing it around Christmas due to it being so inexpensive. Since the early 1990s its copyright has been re-established (see the other wiki for all the details), but it's still a holiday staple, albeit exclusive to one broadcaster.
It was obscure enough in 1968 that Andrew Sarris doesn't even mention it in the Frank Capra entry for his landmark Auteur Theory book The American Cinema. These days it's usually considered Capra's best work.