It's not my intention to split hairs, but I think perhaps "major hostilities" would apply to the unit sizes involved in the hostilities. After all, the use of the word "major" implies a "minor," does it not?

There aren't entire divisions, or even brigades & regiments moving around anymore - most actions are on company or platoon level. Recent action in Fallujah and elsewhere involved battallion sized forces. But that's about as large as they've come in the past year.

Mission accomplished. Taking in the war as a whole, that is a poor choice of words at best and blatantly untrue at worst. And I lean towards blatantly untrue. But you've also got to keep in mind the context. Bush was paying this aircraft carrier a special visit to recognize them as they had been at sea a long long time.

Objective accomplished would have been much better.

And of course it's a quagmire. But I would point out that the shortest way out of a quagmire isn't always going back the same way you came in.