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 is trying to get the TV back to the channel he was watching, he picks up a big remote and finds the channel which the video camera feed is on, but the remote he is holding on the TV is a smaller one. It then cuts back to Malcolm who is moving his hand away from the remote he just put down and it's the bigger one again.
Continuity mistake: In the scene where Lois finds out about Francis escaping, there are three orange mugs hanging from a rack by the phone. When Lois reaches for the phone to call the police, she makes the middle one start swinging. She and Hal sit down, and the end mug has moved from the rack into a box on the kitchen counter. Also, the mugs are hanging still. Towards the end of the scene, the "fallen" mug is back on the rack, and the middle mug is swinging again.
Continuity mistake: When the "Krelborne" teacher comes to the house to tell Lois that Malcolm is gifted, Lois comes to the door naked and puts her arm up on the doorway. On the shot from behind she has her hand low (about where her waist is) from the shot from the front she has her hand up high (above her head).
Continuity mistake: In the scene where Lois and Hal tell Malcolm he is going to the "special class", Hal notes that the pitcher of iced-tea he makes is always empty, and says, "Look at that - gone," before placing the lid back onto the pitcher. Yet, when it cuts to the wide shot of the table, the pitcher lid is by Hal's elbow. (00:17:50)
Plot hole: In this episode Dewey tells Francis that their aunt died from a cat eating her face (or something involving a cat mutilating her face) and we find out this is how she really did die. But then why would it be an open-casket if her face was destroyed?
Continuity mistake: When Julie passes through the kitchen to get Malcolm, Dewey and Egg are in there cleaning the floor they have suds all over the floor, When Julie runs back through after seeing Malcolm in his underwear she slides across the floor, The floor is still completely covered in suds but when she gets up if you look in the background you see the floor with hardly any suds anywhere. She could not have soaked up all the suds when she slid across.