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.]
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: Francis is only allowed to talk on the phone at school for three minutes a day. I think the code gives him free access to talk to his girlfriend.