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.
In the scene where Paul (Cage) is sitting on Mollys couch, the hood on his jacket switches between being folded inwards and outwards.
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.