During a flashback scene where Cassius assassinates an American in Paris, he walks by several patio umbrellas marked with "Beer. Elevated" - a slogan for Italian beer Tappeto Volante. The scene supposedly occurred in 1985, but Tappeto Volante was not established until 2004.
During the car chase near the end of the movie between Shepherdson and Bozlovski, Shepherdson shoots out Bozlovski's window. Shortly after the car is shown from the exterior with the window intact and the next scene from the interior of the car with it shot out again.
Shepardson and Geary chase the suspected Russian agent towards railroad tracks. In front of them is a train moving on one set of tracks. In the next scene they are still chasing him across the same railroad tracks, but now the moving train is behind them.
When Shepherdson approaches Agent Geary from behind while he is walking along the Potomac River, to tell him to drop the investigation, the Detroit/Windsor Ambassador Bridge is clearly visible in the background. There are no large suspension bridges crossing the Potomac River anywhere in the Washington DC area.
Shepherdson and Geary are leaning against the car as Amber's brother pulls up to the trailer parked along on the supposed Potomac River. The landmark towers of the GM Renaissance Center, in downtown Detroit, can be seen on the horizon.
While in his office Ben Geary is looking on the investigation cork-board and in the crime scene section of "Amsterdam" (The Netherlands) there is shown a photo of police men with "POLIZEI" printed on the back of their uniform which is typical for German police not for Netherlands' investigators (name: POLITIE).
When agent Geary has the stacks of dossiers and newspapers strewn across his desk, his colleague comes by, begging for a spot on the team. He picks up an old newspaper and has trouble pronouncing it's name. Geary says "Volkskrant, a daily newspaper in Holland". In the next shot the other agent is shown reading the cover, which is partly obscured, but you can definitely see: "...krante Trouw". Trouw is a different newspaper altogether and the Volkskrant logo has never been in a gothic typeface.
The goof items below may give away important plot points.
Each time Paul used the cable concealed in his watch to garrote a victim, the cable would be covered in blood; and some of it would be emitted from the watch when the cable was retracted. This was especially notable when Tom pulled out the just-used cable and it was completely clean.
The logic by which Geary "proves" that Shepherdson is Cassius is flawed. The "proof" is that Shepherdson is in every crime scene photo, thus proving "Cassius comes back to the crime scene". But as he was in fact posing as an investigating CIA agent, supposedly chasing Cassius, it was not only normal but essential for him to go to all the crime scenes of Cassius' murders.