When Swigert is talking to the NASA doctor, he says "He just wants to be on that shuttle", but Apollo 13 had only a Command/Service Module and a Lunar Excursion Module. No shuttle.
From 02:33 -The computer, Gideon, has been instructed to ignore any inputs from Hunter but she follows his orders anyway.
From 09:12 -at near freezing (or below) temperatures cold blooded creatures (including dinosaurs) would be hibernating; at the least extremely lethargic. If you listen to the dialog you hear that the writers themselves have acknowledged this plot hole.