Plot hole: When Agent Memphis is about to be executed they ask him if he needs to "Piss" so as to not have government-used drugs in his system before he commits suicide. They even mention writing a suicide note for him. He's had seven shades beaten out of him though and was kidnapped whilst on the phone, mid-conversation and with possible witnesses. Surely if it wasn't the first time they had done this then they would have taken more care to make sure it wasn't a complete fake-out.
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.
Factual error: In the mountain scene, Wahlberg shoots a sniper through the scope. This is a common myth in Hollywood. Tested by Mythbusters. It is impossible to shoot up a sniper scope due to the amount of glass and the thickness and angles of said glass. The bullet is deflected, even at point-blank range.
Continuity mistake: When Bob is preparing to shoot, the bolt for the rifle is out, but in the next shot, it is closed.
Continuity mistake: When Memphis is being tortured, you can see when they force him to drink water that they've pulled several of his teeth out. When Swagger rescues him, he has a full set of teeth.
Other mistake: When Michael Pena is looking at the photo of Swagger after winning the Wimbledon Cup, it identified Swagger as "Sgt Major Bob Lee Swagger, USMC, from Gillette, WY." Two things are wrong: (1) Swagger is wearing civvies, if he's in the Corps, he should be wearing his uniform; and, (2) Swagger is supposed to be a Gunnery Sgt, not a Sgt Major. (00:44:20)
Factual error: In the assassination scene, it is shown that the Russian sniper used the Barrett M82A1 in the .60 BMG. There is no .60 BMG. Barrett M82A1 is .50 BMG.
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.