Oops!...I Did It Again - S2-E22
Continuity mistake: This episode establishes that Lily was born at the Live Aid event, which took place in July 1985. In the show's final episode, "Hello, Goodbye", Brad and Lily are graduating in 2005 (see the "congratulations" banner in a hallway at their school). Being born in 1985 would mean that she is graduating at age 20. It is highly unlikely that she failed and repeated two of her school years. Brad, who is the same age, is graduating with her, and he is a dedicated student.
Continuity mistake: When Sean and Claudia catch Lily doing homework in her room, and they realise that she is not actually drunk, Sean asks where she was "tonight." But downstairs, a few minutes ago, Sean commented on her being drunk in "the middle of the day."
Pay You Back with Interest - S4-E7
Continuity mistake: In this episode, Lily's golden sprite tattoo is underneath the name "Dean" - "Dean" is written above the sprite's head, between the tips of her wings. A few episodes ago, at the end of "Your Father Shoulder Know - Part 2", Sean hugged Lily and accidentally lifted the back of her shirt, revealing the tattoo. The name "Dean" was not there.
Suggested correction: People don't always have the time and/or money for a tattoo of that size to be finished in one session. Dean's name was simply not added yet. Or, since the sprite appears to be finished when Sean hugs Lily, maybe Lily had not yet decided to include the name.
Continuity mistake: In the scene when Sean breaks down Lily's bedroom door and catapults into the room, there is a poster on Lily's wall across from her door. The poster goes from hanging properly to one corner untaped as the shot changes.