When Lolita looks through the stacks of $100 bills Humbert has just given her, they are clearly modern notes with design elements and signatures of the 1990s, not the earlier versions that would have been in circulation circa 1950.
When Quilty plays the concerto's opening theme on the piano, his hands are ascending, but the music is descending. However, the piano continues to play when he leaves it, indicating that it is in fact a player piano, and he was not playing the piece at all.
In the jawbreaker scene, the jawbreaker is at first bright yellow, then in the next shot, is white. However, jawbreakers often change color as they are sucked, so it is conceivable that the yellow layer had melted off, revealing the white underneath.
The goof item below may give away important plot points.
Lolita has a poster for A Place In The Sun on her kitchen wall when Humbert visits her to give her the money she's asked for. We later learn that Humbert died in prison in November of 1950, and that Lolita died in childbirth on Christmas of 1950. A Place In The Sun was not released until 1951.