Other mistake: When Lucas is about to take Alexa from her friends, you can hear them re-using an audio clip from a previous episode, "But if I tell them the same thing is gonna happen to me" which would only apply if this was before Alexa tells everyone that she is the one with cancer.
Continuity mistake: I'm not sure what type of mistake this counts as, but in here it is. In the episode "Speaking of Cancer" in season four, Jennifer reveals that she has been lying to Jack and Katie about them all having a shellfish allergy for years because it costs too much for them all to eat it, but in the season one episode "Picture Day" Dave puts down a plate and Jennifer says "Ooh are those crab-cakes?" and takes one to eat. Jack was sitting next to her, so he should have heard this and tried to stop her.