Well, as Americans, we need Congress's approval, which we got. U.N. approval? Not so much.
About the bombs... it's not like we weren't at war with Iraq already, exchanging fire with them every day as part of enforcing the no-fly zones. In fact, by the terms of our truce with Saddam after the Gulf War, nothing less than regime change was already justified by his violations of that truce. We legitimately could--and obviously did--drop bombs on Iraq at any time. Putting the Big Stick on prominent display is part of diplomacy, too. Some would say that it's a part of diplomacy that was long overdue in our dealings with Saddam. If he had taken the message of the bombs to heart, instead of naively believing in the power of French diplomacy to block American beatings, those bombs would've been the end of it, instead of the prologue to what came next.
Anyway, the bombs were appropriate even in the context of enforcing the no-fly zones. If they also prepared the way for a possible future invasion of Iraq, well, that's exactly the sort of eficient use of limited resources that good Generals always strive for.
