Plot hole: The system providing oxygen can only be accessed by someone slim. Therefore John Goodman built the bunker with him unable to access the key facility that provides oxygen in his bunker. Yet he must have been able to go and get Britney when she went to that area?
Suggested correction: It's not a plot hole because he said in the film, the normal hatch to the air filtration was blocked by something that fell on top so they couldn't get through that way.