Continuity mistake: When interrogating Orlov her wedding ring is in different positions when the camera cuts to her.
Revealing mistake: In the White House after they have captured Salt and are walking her chained to be transferred, they meet Ted up the stairs and she chokes him with the chains. Liev Schreiber is replaced by a double with a different hair cut. Ted's hair is short while the double's is long.
Other mistake: When Salt is arrested and in the back seat of a police car, somehow she takes control and causes a lot of smashed up cars, and hits about ten large yellow bins. The problem is: Those bins are there because they have water in them, to lessen the impact of crashes, but there was no water to be seen.
Other mistake: After Winters has shown his true colours, he and Salt are talking through the glass in normal voices.When Salt starts shooting the glass, it is muffled from inside, indicating some sort of sound proofing.
Answer: They have to at least investigate that kind of an accusation, and when Salt so vigorously resists arrest it basically confirms, in their minds, that she is in fact a spy.
Phixius ★
I actually kind of find it shocking that they would be willing to believe a guy who would do or say anything to save himself and since Salt was with the agency a long time, they could have at least given her the benefit of the doubt.