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.
The movie should end in 1952, not 1950. Like the novel, the year is 1947 when Humbert meets Lolita, but the book states that both cross country trips and the time they spend at Beardsley amounts to about 2 years. The film has the same "3 years later" time jump as the novel, but there's no way from summer of 1947 to fall of 1950 could they have spent a year traveling the country, stayed in Beardsley for most of the school year, had another few months on a second cross country trip, and then have Humbert searching for Lolita for 3 years.
When Humbert pours drinks for himself and Charlotte, the glasses are shown with huge cubes of ice and are about 3/4 full. However, when he puts the glasses down in the next shot, there is little ice and the glasses are barely half full.
When Humbert sits down to remove Dolores' shoes (in the hotel room) she offers up her right leg in the wide shot. However, when the shot moves in close you see him holding her left foot and proceeds to remove her shoe.
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.