Agent Sinclair says there are only two variables for the bullet, muzzle velocity and angle of gun. In fact there are many more variables, wind velocity, air density, temperature, and mass of projectile to name a few.
When Charlie talks about GPS, he says the satellites are in geosynchronous orbit. GPS satellites are in orbit approximately 12,600 miles above Earth. Geosynchronous orbit is approximately 22,250 miles.
Alan says the jigsaw puzzle he's working has 5,000 pieces, but that's just not possible. The border is shown complete, and given the size of the pieces and the puzzle's dimensions, 1,000 pieces is much more likely. The box on the table is difficult to read but seems to bear this out; a five is poorly-superimposed over the one.
Charlie mispronounces "Fourier" as "furrier." Any mathematician of Charlie's status would know it's pronounced (more approximately) as "Fouri-ay."