When Mark is undressing to wash his clothes, he strips down to just his boxers and no socks. He then hears a noise, is startled, and goes back to stripping, removing the left sock he had already taken off.
We see Mark place multiple pieces of tape on the picture side of the photo of his wife as he re-assembles it but when the whole thing is shown only one piece of tape (the last one) is visible on that side.
When Mark tears up the photo of his wife he rips it in half three times making 8 parts. When he sticks it back together there are only 4 parts (ie 2 rips). This is untrue. After ripping the picture in half Mark then rips both halves separately, so he should indeed end up with four pieces.
It makes no sense that Mark S. should be able to enter the severed spaced while carrying Graner's swipe card. The entire operation relies on the Severed not having any information about the unsevered world, which is why there is surveillance so good and effective it even detects small scraps of paper they might have ingested and such. The swipe card would be much easier to detect than that. It could even be achieved with current-day non sci-fi technology such as RFID chips or transponders.