Revealing mistake: When Becky climbs through the door and falls upwards a lump appears on her back revealing where the wires are attached as they pull her up. (00:02:40)
Continuity mistake: When Simon meets up with the "second" Jerry he throws him to the floor making Jerry almost falling through the door. Then Simon grabs Jerry with his left arm, but when it cuts he is holding onto Jerry with his right arm. (01:04:05)
Visible crew/equipment: When we first see Kate, she opens a door, and then, she climbs through. As she climbs through, you can see down her blouse, and you can see a microphone. (00:07:30)
Continuity mistake: When Kate is climbing up the ladder to see where Max keeps disappearing to, the left half of her outer tee-shirt alternates from tucked into her trousers, to hanging out. (00:09:55)
Continuity mistake: At the end, when Kate is standing on the edge of the exit of the Hypercube, you can see her through the exit in the shots from below. In the shots from the top however, the black door of the exit is still closed. (01:22:35)
Continuity mistake: When Simon and Kate get separated the first time Kate opens the door and lowers her hand. When it cuts she still has her hand up. (00:10:00)
Continuity mistake: After everyone releases the colonel from his belt and lay him on the floor, Simon takes out his identification. Between a wide shot to a closeup, the top of the colonel's shirt goes from being tucked under his tie, to being untucked from under it. (00:14:30)
Continuity mistake: During the movie, Max's shoes change, and they obviously can't because he's trapped in the hypercube. When helping the colonel who's hanging himself, you can see Max's shoes are black, but then later on they're blue. This is most noticeable in the scene when Max and Julia are talking, and Max throws his shoe across the room. (00:13:45 - 01:08:10)
Continuity mistake: When Simon first takes Kate down, he covers her mouth with his hand, then with the other hand, holds a knife. In one shot he holds the knife to the side of her face, but in the next closeup shot, he has the knife resting on his other hand, which is covering her mouth. Then in the next shot he is holding the knife to the side of her face again. (00:08:10)
Revealing mistake: When Kate opens one of the doors to find Simon on the other side ("Hello gorgeous, miss me? Huh? Come on in, the water's fine."), the shot of her climbing up to open the door is a recycled shot from 42 seconds earlier. It's pretty obvious as the shot still contains a mistake from when the shot was used previously - a boom mic is reflected in the door's shiny surface as Kate climbs up to open it. (01:18:40)
Continuity mistake: At the end of the movie when Kate is killed from behind, the number and positioning of soldiers in front of her is completely different in the shots immediately before and after Kate's death. (01:29:00)
Revealing mistake: When Kate is in one cube room on her own, looking around, just after losing Simon and just before meeting Sasha, as the camera pans around the room, on most of the black cube doors, clearly reflected on the shiny surface of them, are camera / stage lights. (00:10:15)
Continuity mistake: Throughout the movie the blade on Simon's knife changes. In some shots it's a double straight edge blade, in others it's serrated on one side.
Continuity mistake: The position of the 'rope' of clothes on which Simon is holding changes. In one shot he is holding onto a particular part of a shirt, but in the next he's holding onto a different part. (00:31:05)
Continuity mistake: When Sasha is trapped in the Razorsphere room, she yells "Kate, help," and then between three shots her necklace changes from tucked under her purple shirt, to hanging out and back to tucked under. (00:54:20)
Continuity mistake: The blood that Simon wipes off the knife onto his hands disappears instantly. (01:04:30)
Continuity mistake: When Colonel Maguire lies down on the floor he prays and folds his hands. When it cuts to a wideshot you can see that he isn't folding his hands anymore. (00:07:05)
Revealing mistake: After Kate kills Simon after he kills Sasha, the small hands on the four watches that he is wearing move at different times to each other when they are supposed to be synchronised.
Visible crew/equipment: As all the different realities start collapsing into one space, Kate goes to open one of the doors. As she climbs up to open it a boom mic is reflected in the door's shiny surface.
Continuity mistake: When Simon breaks Sasha's neck, she falls to the floor, and lands face down. But during the fight between Kate and Simon Sasha's head is now facing to the side. (01:20:35 - 01:21:40)
Chosen answer: I'm inclined to think it was longer than a month because of the lack of proper needed care for such an injury would prolong the healing process. But he only had a handful of souvenirs on him, which means he probably stopped collecting after a while. I concur with your cannibalism theory, there's no other way he would have survived. However that doesn't explain what he could have done for water. This theory of Simon spending possibly months in the cube also brings up the question: If the cube breaks down at 6:06:59, then how is it possible to live in there for months? Well, as we saw, certain rooms have slower and faster rates of time. So, he could have spent all that time in a room with a slow time rate waiting for people to wander into it and feed off of them.