Other mistake: When Johnny and Mark save Denny from Chris R., they claim they are taking Chris R. to the police station. However, they re-appear in the scene almost immediately after (within 2 minutes of screentime, which is meant to be in real-time), with their having been obviously nowhere near enough time for them to have taken Chris R. to the police and done the appropriate interviews/paperwork.
Audio problem: Much of Johnny's dialog is dubbed in throughout the film, with his lips and dialog not quite matching. (This is due to actor/director Tommy Wiseau's thick accent making the original dialogue sometimes hard to understand).
Factual error: When Johnny commits suicide in the end, the slide of the pistol doesn't move when it fires. (01:33:00)
Other mistake: When Johnny first goes into the flower shop to buy roses for Lisa, the clerk says she didn't know it was him. As he is leaving, she says he is her favorite customer. If he's her favorite customer, then there's no way she couldn't have known it was him, especially given how unusual he looks and sounds.
Character mistake: When Lisa first seduces Mark, Mark notes "The candles... the music... the sexy dress... What's going on here?" However, there are no candles and there is no music playing at the apartment during the scene.
Factual error: The way Johnny records the phone-calls makes no sense whatsoever. He plugs in an old cassette-tape player/recorder to his phone, puts a single tape in, yet we're expected to believe it is always recording, and never fills up. Tapes don't last long enough for him to record days of audio, nor will lazily "plugging it in" to the phone record all of the phonecalls.
Other mistake: You can tell that Johnny and Lisa's second love scene re-uses several shots from their previous love-scene, and also includes alternate unused angles from the shooting of that scene. Watch for the rain running down the windows to give it away.
Continuity mistake: After Johnny and Mark return to the rooftop following the "Chris R." sequence, we see Johnny run into frame, and Claudette is standing by herself to the side of the others. Mark is not on the roof yet. Immediately after during the next few shots, Mark suddenly appears behind Claudette, and even has his hands on her shoulders.