When Carson and Hulse enter Richard's apartment, they crash through the kitchen windows, showering the room with broken glass and wood and tearing down the curtains. A few minutes later, Richard and Morris each enter the kitchen and notice nothing amiss.
During the scene with the dead bodies in Richard's apartment, Reese manages to remove all the shelves and food from Richard's refrigerator, hide them somewhere else in the kitchen, stuff Carson's body in the fridge, then remove the body and put all the shelves and food back - all in a matter of seconds.
Cooper isn't wearing sunglasses as he chases Richard and Maddy in the federal building at the end of the movie. When he bursts into the senate hearing room, gun drawn, his sunglasses are suddenly back on and he has to flip them up.
When Richard rides his bicycle from his apartment and stops at the junction the wheel of the car behind him has driven onto and is between 2 yellow lines. Change camera, the car is to the side of the yellow lines and is not yet on the lines.
When Maddy leads the team into Richard's building she's carrying a clipboard and has no gloves. She's carrying a case hanging from her right shoulder. When she walks into his apartment, the case is hanging from her left shoulder, she's lost the clipboard and gained a pair of gloves.
The subway system used should be the WMATA (Washington Metro Area Transit Authority) Metro system, because they are obviously in Washington, D.C., but the Metro will not allow scenes on their system which have weapons or chases. The Los Angeles Metro was substituted for it.
The assassins in the film used revolvers with silencers. It is nearly impossible to silence a revolver, due to the gap between the revolving cylinder and the barrel, which allows sound waves to escape.
When Morris crashes his bike into the lake (chasing the ambulance), the stuntman is holding handlebars in his hand as he back-flips into the water. Look closely, and you can see handlebars still on the bike he "crashes".