Continuity mistake: When Matthew Broderick is watching his girlfriend on the wall with his camera, he starts painting the wall white. After he gets a good patch painted, they go in for a close-up. The close-up however is of him painting the wall from a few seconds earlier. You can tell this by his girlfriend making the same head movement, right before they cut to the close-up and the roller going in the same direction as it did before the close-up.
Factual error: At the start of the film, they are using an optical telescope for astronomy in daylight. This is not possible. The telescope is also far too small to be giving such a detailed picture.
Audio problem: When Anton is walking through the park and Maggie and Sam had just bribed the street performer to allow them to put lipstick on the monkey, you can hear applause although none of the onlookers were clapping. This happened when the monkey initially jumped onto Anton. It was only after the monkey jumped off and Anton acknowledged the onlookers did the audio match.
Factual error: In the scene when Maggie goes to the building rooftop to set a listening device to eavesdrop on Anton and Linda, she sets up what is presented as a parabolic microphone. However, the device she sets up is actually a radio frequency (RF) micro-wave style antenna that would be used for point to point RF communication. An audio parabolic microphone would be a round, solid dish shaped design to reflect the audio waves to a highly sensitive microphone at the focal point of the dish. The RF antenna used in the film would not capture any audio.