When Brennick meets Teller, Teller states that he was the prison director in charge of the original Fortress which Brennick and his wife escaped. In the original film, the prison director in charge of the Fortress was Poe.
Christopher Lambert's character is billed as John Henry Brennick, however during the scene where ZED is processing Brennick into the fortress, he is referred to as "Brennick, John W.".
The nose blood from Brennick's short time in space without a suit disappears after he closes the tunnel's airlock during the rapid decompression from the airlock chamber door blowout.