When Rimmer's alarm goes off at 6, it is 6 am as breakfast then mentioned but the alarm setting on the left shows 1800 which is 6 pm.
Cable used to control Holly's motorised monitor can be seen moving on the floor after he moves off in the scene where Rimmer's legs are separated from his body. It can also be seen trailing along the floor at the beginning of the next scene.
When the meteor hits the ship and everything shakes, the pieces on Rimmer's draughts board don't move at all, they've obviously been glued down.
When Holly and Queeg are playing chess the other monitors show a virtual board and positions of the pieces of their game. When the game finishes and Queeg wins by checkmate, the board seen on the monitor shows a position where all the pieces are close to their starting positions, on their original starting side, not a winning checkmate position.
When Holly's motorised monitor moves into the corridor and he says "Halt, dudes", his lips don't move.
Immediately after the Cat gives Holly advice on playing chess, a crew member's hand can be seen on the supposedly computerized chess game screen.