There probably is some test of some sort. Not the same as the Chuunin exam, but a test nonetheless. I'm betting you have to perform a certain level of mission, too. Or, at least, do something extremely hard and get recognized for it. Making it based purely on the number of missions means that you can have someone do a lot of low-level missions and eventually become Jounin. Even performing a certain number of high-level missions can be a little iffy, because sometimes a high-level mission is easier than people think it will be (and vice versa - remember the first "real" mission Naruto/Sasuke/Sakura went on? Hehe). I'd bet that there is a combination of things you have to do, like a certain number of missions, a really hard mission, and passing a test, before you're allowed to become Jounin. Letting the Hokage choose who gets to become Jounin sounds a little too much like favoritism...

Then again, the previous Hokage gets to choose his successor, right?