Deliberate mistake: The turn count for Lisa's stay in the Cryogenic Sleep Chamber is off. The card reads she should be there for 5 turns. 'Turn' can either represent a single move made by either Danny or Walter, or a complete game cycle where both Danny and Walter have made a move. If we count the turns by player, it comes to 8 and she's awake 2 turns too late as it should have happened at the start of 6th. If we count both players' moves together as a start of a turn, then she's awake 2 turns too early as its turn 4 and not turn 6. It seems obvious from showing us the shower suddenly start up that this is the correct point in the film they wanted her awake, so it's unlikely she was actually awake off-camera during the Astronaut's arrival and we just didn't see.
Continuity mistake: When Walter and Danny are trying to show Lisa what the Zathura game does, Walter lays the "Promoted to star ship captain" card on the game board in front of the card console. Two shots later the card vanishes. The camera had only changed for two seconds, so it's unlikely that either of them had enough time to take it away.
Revealing mistake: When Walter, Danny and the astronaut are in the kitchen breaking stuff to burn, the smaller boy tries to smash an old style broom on the table. He tries three times, on his final try the shank breaks in half, revealing where it had been sawn nearly all the way through in nice clean line, with only a splintery piece showing where it really snapped.