The ribbons on the Marine uniform Agent 47 takes are anachronistic, since they contain Gulf War medals and the uniform is that of a gunnery sergeant. A gunnery sergeant can only serve 22 years at that rank before being discharged and the Gulf War took place 24 years before the movie's release.
When Katia and Agent 47 arrive in Singapore, they spend a night in a hotel. Agent 47 goes to sleep and Katia goes for a night swim. When she leans over the pool's side, it is clear there is no wound or scar on her upper right arm where 47 "marked" her with his bullet.
Exactly at 48:08, John Smith shouldn't be able to grab the gun from the dead squad without pressing the safety release button on the holster. As we can see, the holster has a safety button on the side to lock the gun.
Singapore is a country with right-hand drive cars on the left side of the road, though left-hand drive cars are allowed in Singapore. In the chasing scenes in Singapore, the red Audi and villains' SUV were left-hand drive cars.
After the Helicopter that brings Le Clerque and Litvinenko explodes and is engulfed in flames, we see that the traffic below, especially in the bridge and the main road, are driving on the right side. This scene is supposed to have been shot at the Syndicate International HQ located in Singapore, a country which drives on the left side of the road.
When at the embassy, agent 47 is wearing a Gunnery Sargent's uniform and a Marine asks him "is everything alright sir? Sir?" Gunnery Sargent is an enlisted rank and would not warrant being called "sir".
The are two main mistakes regarding the car chase scene. First, the cars, the Audi and the Mercedes Benz G-Class, have the steering wheel on the left side.This scene is set in Singapore, and although you're allowed to drive a left hand drive car there, the more common use would be to use right hand drive cars. Second, the license plate of Agent 47's Car, the Audi, is totally wrong. The license plate of the car is SGE-1815 G. The second and third letters (GE) are assigned to Light Goods Vehicles, not private vehicles. The right combination for a private vehicle would be S (B to Z) (B to Z) followed by 4 digits and one letter for example: SDN5145G.
When John Smith goes back to Katia's apartment to try and find out where her father is, (51 minutes in) he takes out his phone to let his boss know that he is in Singapore. As he puts the phone up to his ear, you can see that he didn't actually dial anyone, the screen still has the home screen icons on it.
Agent 47's pistols are .45 caliber. When he goes to the American embassy and spreads his arms revealing his weapons to the guard at the metal detector, the the magazines in his pistols can be clearly seen to be stamped ".38 Super" while the magazines on his belt have ".45" stamped on them. A .45 caliber round and .38 Super round cannot be fired by the same pistol, so the two extra magazines on his belt are useless.
When Agent 47 and John Smith are being detained at the embassy, Agent 47 finds a way to fire his sniper rifle. When he does, the bullet reaches the glass behind him and cracks it. In the next scene John Smith jumps into the glass breaking it completely. This type of glass is bullet-proof and shouldn't be able to break like that.