The state of residence of the trustee could have an effect in that  if the trustee does anything wrong or improper, or there is a challenge to his actions, depending on the exact circumstances of the issue/challenge/etc., it may be that any legal action would have to be filed in his state (and take place under his state's court rules and possibly law), which may be inconvenient for the beneficiaries. (To oversimplify, the rules for jurisdiction, or which court has power, and venue, or where the case should be heard, reference, among other factors, the place where the defendant or person against who the action is brought lives.) However, this is easily dealt with: the trust instrument can specify which states law applies and also where any cases will be head (e.g. it can state to apply the law of a given state which you know is favorable, and also state that the case will be heard wherever the benefiary lives), and such "elections" in the trust instrument (document creating the trust) are valid and enforceable.