Yes. A dropped foul ball can be considered an error if the official scorer deems that the player should have caught the ball. The batter will not reach base in this case. However, if the batter subsequently scores a run, the run will be unearned.
Notably, an error on a dropped foul ball would not disrupt a pitcher's attempt to record a perfect game.
Chat with our AI personalities
Yes. For example, if the batter pops up into foul territory behind the catcher, the catcher can be scored for an error if he gets under the ball, the ball drops into his glove, but he then drops the ball. The batter gets another chance to bat, but no matter what happens later in his at-bat, the run will be unearned due to the catcher's error.