In the beginning, Evelyn Salt is shown to be extremely worried about her husband's wellbeing. We later find out that she wasn't faking it. Because of him, she stopped her mission to kill the Russian Prime Minister, even though she knew that she wasn't supposed to marry someone unless it would achieve their goals. So when she found out that Orlov had her husband, she had to pretend to kill the Russian Prime Minister and succeed her mission so she could gain Orlov's trust and get her husband's location to rescue him, but things didn't go the way she planned...
At the start of the movie, Orlov manages to escape the CIA by killing two agents in the elevator with a knife concealed in his shoe. Wouldn't the CIA have checked for things like that when they brought an enemy spy in to be questioned?
Quite a few cases, but perhaps the most notable - The President was awake when Winter revealed his evilness and while this wouldn't necessarily prove Salt's innocence it, in combination with the many other factors, could easily clear her name.
The Director's Cut explicitly says the President was killed, changing the ending considerably.
The scene where she checks into a hotel under a false name wearing a jacket she stole. Once she's in the room she goes into the bathroom and removes her false teeth and colored contact lenses, demonstrating how she is Crazy-Prepared. At first you watch and you're like "Wow she's a master of disguise! I didn't even notice the (now obvious) fake facial features!!" but then you realise that the reason you didn't notice her disguise is because she looked exactly the same and was completely recognisable.
But it becomes Fridge Brilliance when you realize that she wasn't wearing those things to disguise herself from her pursuers... she was wearing them as part of her cover, in order to resemble the real Evelyn Salt, the American girl she replaced as a child.