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 two-way mirror scene, Carson calls Richard's violin 'some kind of banjo'. However earlier in the film he had no trouble identifying Drew's violin case.
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.
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.
When Richard stops his bicycle at the junction the reflector on his front wheel is below the axle. Change camera, the reflector is above the axle.
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 is taking a pee and the bathroom door swings shut the "dead" agent hanging on the back of the door lifts his head and looks at Morris.
When Richard arrives home after the dentist, thick knee pads can be seen under his pants as he sets the kickstand on his bicycle. This is because shortly after entering the apartment, he is shot with tranquilizers in the buttocks and Tom Hanks falls to his knees and then his face without the aid of a stunt double.
When Morris crashes his bike into the river (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".
In the scene with the subway train, the destination board reads "Special".
When Paula is climbing down from Richard's window, her hair is differently colored than in the previous scenes, meaning it is obviously a stunt double.
When Morris rides his bicycle over the picnic table and into the river, the ramp behind the table that the stunt double used to launch himself into the air is clearly visible.
When Richard and Maddy come out of the Washington Metro (subway), they are instantly on Capitol Hill. The Red line from Dupont Circle would take them to Union Station, but it's several blocks' walk uphill to the hearing room--though the audience might not have been shown all that.
The music that Richard Drew writes on his bathroom mirror isn't the music he's humming.