But then usually/often even if I am clicking way down the right side of it, it reacts as a left click. I found if I use my first finger on my right hand to click it, it works fine. (That's really stupid!!) It means, I am right handed, so my first finger is over the left button, my second finger over the right button. If I use my my second finger on the right button, usualy it will be a left click. If I awkwardly use my first finger to stretch over to the right click, it works fine.
The reason is works when you use your left mouse button finger is because you then have no finger at all resting on the left hand side.
The way the mighty mouse works is this: There are two little pads, one in each side, that work like the iPod click wheel. They detect which fingers are touching the mouse. If you have the 'right click' functionality set to secondary button, the following guide will work:
index finger on left, middle finger on right = left click
index finger on left, nothing on right = left click
nothing on left, middle finger on right = right click
You have to physically not be touching the left side at all. It's not about whether there is pressure or not. The mouse can detect your finger resting on the left even if you aren't actually applying any pressure.
I never have a problem right clicking with a mighty mouse. I don't own one because I don't like them. So remember, just lift your index finger up away from the surface of the mouse and press the right side with your middle finger and you'll get a right click.