Revealing mistake: When the police dog wants to attack Swagger and bites the cop instead, it's obvious the cop wears thick protection under his coat sleeve. (01:03:20)
Revealing mistake: When Swagger is going to see the Russian sniper, the bait, he takes out one of the guards with a wire around the neck. The only problem here is that the wire isn't even close to the guard's neck. (01:26:10)
Revealing mistake: In the stolen FBI black car Mark Wahlberg is driving over the guardrail into the river the trunk flies open, revealing the inside of the car trunk. The mistake is that everything inside the trunk has been stripped out including the carpet because the car is going to be in the water for the film.
Revealing mistake: When Swagger is on the mountain and looking though his scope at the guy with the shotgun, the audience is shown what Swagger sees though his scope. However, the pictures we see does not match that very telescopic view Swagger would see at that distance but instead something shot with a relatively wide angle lens at close distance.
Answer: He's looking for callouses on the hands. Professional snipers end up getting hard skin inbetween the webbed part of the skin between the thumb and forefinger because of constant rubbing on the trigger guard. By checking the hands, he could tell whether or not he was talking to a proper sniper, and in particular Swagger.
GalahadFairlight
The webbing between the thumb and forefinger would rub on the stock or grip not the trigger guard.