When Maurice pulls down Brian's pants, he gets embarrassed and yells at Maurice saying that no one ever sees him in his boxer shorts - not even his mom. But, on the first night Brian follows Maurice to Monster World, he ran around in his boxer shorts all night.
Brian takes a Polaroid picture by holding the camera in front of himself while in the classroom with Kiersten. Later in the movie, the photo is on Kiersten's nightstand but he is posing with his arms folded.
During the montage of havoc from Brian's first night with Maurice, his clothes change to what he wears the second night, then back to his clothes from the first night.
When Brian and Coleman are fighting at the school you can clearly see Brian knock Coleman's hat off and see the hat fall. However, when the Principal is walking towards them and they're shown fighting again, the hat is back on Coleman's head.
When the monster melts at around 28 minutes his clothes change position and location in the room.
When Glen is flipping through the channels without the remote, he puts on a Celtics game, and then a Phillies game in which Harry Kalas announces Mike Schmidt's name. Later, Glen asks Brian and Eric if they have seen the remote because he wants to watch the Sox and Celtics games. However, interleague play did not begin until 1997, so there is no way the Red Sox could play against the Phillies.
While it is understood that Brian should not visit the Monsters' world anymore because he may turn into a monster himself, there is no reason to think Maurice cannot continue to visit Brian at night in the human world. This makes the tearful goodbye at the end unnecessary.
The first time Brian enters Monster World he asks Maurice "What is this place? I thought the dining room was under Eric's room." However they entered from under the bed in Brian's room not Eric's.