If a will names you to serve as executor, the probate court will probably appoint you to the post without any problem. There are circumstances, however, in which certain people may not be allowed to serve. And if you're from out of state, the court may impose requirements and restrictions on you that wouldn't apply to an in-state resident.
Executors can always be removed from their post, as well. If an executor messes up badly--for example, uses estate funds for personal purposes, or doesn't provide accountings required by the probate court--the court can take away the executor's authority and appoint someone else. Usually, unhappy beneficiaries are the ones who push for an executor to be removed.