When Mary and George are walking down the street after the dance, she asks him, "Well, why don't you say it?" The next shot George is heard saying, "I don't know. Maybe I will say it," but his mouth is not moving at all.
When Mary puts on "Buffalo Gals" on the phonograph, she starts a ten-inch, yellow-labeled record, but in the next shot, a dark-labeled record is playing. Also, when Mary breaks the record after the conversation with George, she breaks a twelve-inch, yellow-labeled record instead of the original ten-inch record.
After Clarence disappears while being wrestled by Bert the Cop, you can see the shadow of Ernie the Cabdriver, shaking his finger. However, when the camera shows Ernie, he has both hands on the tree, and then he begins to shake his finger.
As Violet walks away from George, Ernie, and Bert, Ernie watches her out the window of his taxi. He stops watching and moves away from the window. In the next shot, he is watching from the window again.
As George approaches Bert and Ernie by Ernie's taxi, and then all three ogle Violet as she walks down the street, the same woman in a print dress, holding the brim of her hat, walks by five times in 30 seconds.
As George and Mary prepare to drive Martini's family to their new home, Mary (in a close up) is holding the goat's horn/antler. The scene cuts to an extreme long shot in which her hand is nowhere near the goat.
When George and Mary are throwing rocks at the dilapidated house on the way home from the dance, when George throw his rock, the window that Mary is supposed to throw a rock at is missing. Then when Mary gets ready to throw her rock the window is there.
When George invites Carter to come in and follows him, he is holding the pipe with his left hand. But in the shot after someone asks him about hang up the phone, he appears with the pipe in his right hand.
When George visits his father in his office and finds him arguing with Potter, his father is standing behind his desk talking to Potter. There is a cut away form this but upon return George's father is now on the same side of the desk as Potter.
In the drugstore when Mary leans over the counter to whisper in George's ear, a piece of tape suddenly appears on the edge of the counter between George's and Mary's heads. This was most likely done as a reference mark for the young actors so the focus puller could accurately pull focus.
When Mary (Donna Reed) throws her rock at an upstairs window of the dilapidated old house, the rock disappears a split second after leaving her hand, and then reappears in the distance just before crashing through the glass. The roof of the house was a matte painting, added after principal photography by the visual effects department. When Ms. Reed threw her rock (and it was her throwing it, not a stand-in), the arc of its flight was a bit too high, and it crossed the matte line for most of its travel. Consequently, it was covered up by the painting, which was added later. Apparently the live-action crew did not notice the potential problem when filming the shot.
When Uncle Billy is counting the money at the bank for the deposit we can clearly see the first few bills are 5's, followed by at the most 20 more bills. Considering that these would have been monthly cash payments on $6000 mortgages it is unlikely that anything close to $8,000 could have been in that small stack of bills. It is about 1/3 of the size of the wedding money which is 1/4 of the amount.
The goof items below may give away important plot points.
On the tombstone, Harry Bailey's years of life are show as 1911-1919, which would make him, at the oldest, eight years old when he died. However, immediately before George Bailey brushes away the snow to reveal the dates, Clarence states that Harry died when he was 9, showing that Clarence isn't numerically inclined.
In the first scene where George finds his brother Harry's grave, the year of death (1919) is clearly visible. The next scene, it is obscured by snow and George has to dig it out to find the year his brother died.
When George Bailey is arguing with Mr. Potter in the board room after Peter Bailey's death, George says to Potter: "What'd you say just a minute ago? They had to wait and save their money before they even ought to think of a decent home." We never hear Potter say this, but it is possible that it happened near the beginning of the meeting, which we did not see.