In the scene where Paul (Cage) is sitting on Mollys couch, the hood on his jacket switches between being folded inwards and outwards.
In the opening credits, it is shown that Paul has a Doctor of Science, but later in the movie he claims to have a PhD.
Contrary to what Prof Matthews says, a zebra's stripes do provide it with a degree of camouflage. Seen from a distance through the heat haze of an African plain, the zebra's outline becomes blurred and indistinct.
Paul asks if the bicycle is a fixed gear; when anyone familiar enough with bikes to know about fixed gears would instantly see the derailleur arm, obvious even to the audience in the short split second cut away to a shot of the bike, and know that it's not.