I played with a Mac a few weeks ago when a local store became a Mac retail center. It had that mouse. I don't know if Mac people just have a desire to be different, but that stupid thing was probably the worst part of the user interface.
First, there aren't any "buttons" - you press down on the mouse and the whole top "clicks". Which means you get a click any time your hand puts any kind of pressure on the surface on which it's resting. I had no idea about the "right-click" functionality but I thought Macs were single-button machines anyway so I don't know what good that would do.
Second, and more annoying, was that little scroll-ball. In theory, it's an intelligent improvement to the scroll-wheel that's in common use. But the implementation is absolutely terrible. The stupid ball is literally smaller than a BB and has no resistance whatsoever! You can't control it in any meaningful sense of the word. It would be a nice idea if someone would implement the same idea with a ball big enough and with enough resistance to control. It's also quite schizophrenic in that it works two-dimensionally in some windows and some applications, one-dimensionally in others, and not at all in still others, but that could be a software problem.
Sorry for the rant. It was the first time in a year or two I'd tried to use a Mac, and while the GUI itself was pretty much as I'd remembered it, I was quite stunned that Mac would release such a terrible product as the default mouse.
Strange... Just recently one of my clients installed seven new G5 iMacs... which included the Mighty Mouse... to replace the aging G4 iMacs. The seven women who use them had absolutely NO problem in adjusting to the new mouse although they had been using the single button mouse for years. They really appreciated the new functionality of the scroll ball.
Macs have not been "single button" only machines for years. Simply plug in a multi-button mouse and it works. The right click brings up contextual menus, just as it does on a PC. As to whether it works in a specific application, that is dependent on whether the app is native OS X and followed Apple's programming guidelines. Almost all "Classic" apps (OS 9 and older) will not use the ball.
I suspect that someone may have adjusted the mouse you were using to be far too sensitive to movement.
I've been using the "mighty mouse" since October. I like it. The scroll button works well for me, with just the right amount of resistance. Of course, the only buttons I use are the main one and the scroll button. I have no use for right or left clicking.