Visible crew/equipment: When Dewey yells for Lois because the bow was put on the present, if you look to the left of Lois, you will see a crewmember kneeling down, handing Lois the Red Dress, who is holding a bucket of water. He quickly gets out of the camera's view. [This is on the DVD of the first season. Someone said on the audio commentary that after catching it, they deliberately left it in to see if anyone would spot it. It's still a mistake, but that's why it's there.]
Long Drive - S4-E11
Visible crew/equipment: When Lois is yelling at the boys there is a camera visible on the left side of the frame. (00:01:40)
Visible crew/equipment: Towards the end, right after they watch the house blow up, you can see a hand holding a black object popping up from the right side of the screen. This happens right before Malcolm says, "Pretty sure".
Visible crew/equipment: When Lois gets in the car after she gets offended by the fact that everyone in the family forgot her birthday, you can see a cameraman with the camera reflected on the rear window when she leaves. (00:10:15)
Other mistake: At the beginning of the episode when they are driving in the car, the door is opened to make room for the camera outside but the opening is visible in shot. (01:49:00)
Continuity mistake: When Malcolm and Reese talk about April at the water park, there's a girl with a blue shirt and a towel tied around the pelvis who passes behind Malcolm twice in two different shots.
Answer: Actually, the band is called They Might Be Giants; the song is called "Boss Of Me."
Xofer