I have the same problem, checked in three different computers. One Dell laptop, Acer Laptop and a Dell Desktop. I'm using LMDE 201204 MATE.
Every time I start a MATE session, MintMenu does not open with the first click (you just see the menu shadow). From the second click on it works right.
The problem began when I activated Compiz and It occurs in all computers at home with different graphics cards. I've tested it in both real and virtual machines with the same result. If you deactivate Compiz, the problem cease. Using xcompmgr composite instead Compiz also fix the problem, but xcompmgr is not integrated in MATE.
It's just an annoying bug. Any idea?