Great question! I see three sets of challenges associated with this plan:
First, the technical/engineering aspect. Musk has proven again and again that SpaceX has the technical and engineering capability to pull of spaceflight. Couple that with the fact that the United States has been sending probes to Mars for over fifty years, and it is pretty obvious that from a technical/engineering standpoint, Musk and SpaceX are able to pull it off.
Second, the financial aspect. SpaceX is 100% backed by Musk's billions. That means that if he wants to pay for it, he can. Of course, SpaceX has partners working with them that are helping to reduce costs. But really, Musk could likely write a check for the whole thing himself, which virtually eliminates any problems related to financing the venture.
Third, the legal aspect. This is the most challenging to overcome. SpaceX is a U.S.-based company, and subject to the laws and regulations of the United States, specifically the Federal Aviation Administration. Will the U.S. government sign off on a potentially hazsardous manned mission to Mars five years from now? There are a number of factors at play with that, and Musk cannot control them.
I believe that Elon Musk and SpaceX have the capability and the money to pull off a manned mission to build a colony on Mars by 2022. Therefore, the only question is whether he will be allowed to do it.