Right -- you shouldn't have to start MathType separately. If it's running, fine, but if it's not, it will start when you first use the Insert MathType Equation command.
All the posts and replies have been helpful, but I'm still getting mixed results. The first document I opened in Pages 5.0 was one that I created in Pages 4.3, and it had several MathType equations in it. I could not edit the old equations, but I could insert new ones and edit them once they were inserted. I later rebooted and opened the same document (which was now saved in Pages 5.0 format), and I got a message saying some of the images had been deleted. All of the original equations had been replaced with empty placeholders (gray boxes with a large X), but the new ones were still there.
I haven't been able to duplicate that behavior with additional "old" documents. I can open Pages 4.3 documents in Pages 5.0, and all the old equations are visible and editable. Someone mentioned re-installing MathType, and I must say that I did that (for a different reason), so I must consider the possibility that this had some bearing on the outcome, but I can't be sure.
It does appear, as has been reported many times, and as Peter alluded to above, that you can't add equations or other objects to text boxes or tables. I believe this was intentional on Apple's part, but that doesn't mean it was a good idea.
That said, and this is a Pages thread so I won't say much about it, I haven't seen any problems at all with Keynote 6.0 and Numbers 3.0, when it comes to how they deal with MathType.