Revealing mistake: In an imagination sequence Reese and Malcolm are throwing around Jamie, but you can see it is a doll.
Revealing mistake: When Lois confronts Susan about not telling her about Susan's kidney disease, Susan is telling Jamie how cute he looks in his sailor outfit. When the camera is moved to a different angle, it becomes very obvious that "Jamie" is just a prop baby doll. (00:11:10)
Experiment - S5-E18
Revealing mistake: In the first scene, Lois is feeding Jamie while talking to Dewey. In the next clip, it changes to just a prop baby doll toy with a beanie covering a majority of his face. (00:04:25)
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.