In the final scenes of Inception, Saito is seen making a phone call after the completion of the job. Though we don't hear any conversation, we can assume that he is taking care of Cobb being able to get through customs.
Obviously, Saito is very powerful and very wealthy ("I bought the airline") but what resources does he possess that allow him to completely erase a murder charge?
Saito obviously knows all the ins and outs of dream sharing and extraction and one would assume he had done his homework on Cobb. This is demonstrated by his consideration of him for the inception attempt and is also revealed when he lets Cobb know that he is well aware of his US immigration difficulties and the charges against him, which he promises to 'fix'.
With these unique insights into both the Cobb character and the mechanics of the dream sharing world and its pitfalls and foibles, it is entirely possible that Saito could have used his influence to explain how Mal's death was not Cobbs fault and may have simply held back on authorising the immigration as collateral for the success of the Fischer inception job.
It is not laid out in any detail as to how he deals with this particular issue but considering how powerful and influential Saito is coupled with his unique insights into the films aspects and concepts then he appears to be one of the only people capable of helping Cobb in this manner.
Saito could have arranged a pardon for Cobb from a state governor. That would permanently solve his legal problems, and the deal could be sealed in just minutes.
In exchange, Saito could have pledged to deliver either new jobs or better energy prices to the state, either of which a state governor would be glad to have, especially if the cost is a pardon for one fugitive with no other criminal history, one whose murder case could be hard to prove at trial.
This is not that far off from how some American defense contractors operate: they make sure to establish offices in every state, so that they can threaten local politicians with layoffs and a local economic downturn unless they get favorable policies.
And who's to say that pardoning Cobb would be an unjust trade, even if he were guilty as sin? Wyoming was the least populous state around the time the movie came out, with about 500k residents -- that's a lot of utility to weigh against one murderer. The Framers of the Constitution famously believed it was better to let one guilty person go free than to wrongly imprison one innocent person, and our legal system was designed with just such a bias.
American politics is run by money & self interest. Being rich and powerful Saito will have US politicians in his pocket who will bend the law for him.
Helping him the straight way as has been suggested would need a trial and a court of law, not a phone call. There was 10 minutes till landing from when he made the call?
