Here's a simple one-finger solution for Mighty Mouse right-click problems: Use only your index finger for both buttons. Using the index finger for left-clicking and and right-clicking provides reliable operation of the buttons on both sides of the mouse.
Your thumb should not be further forward than the side button on the left side of the mouse. The position of the fingers on the right side of the mouse is relatively unimportant.
For left-handed operation, I could only get the left side of the mouse "unblocked" by lifting my hand completely off the mouse. It seems the area behind the left side button affects the sensing of the buttons as much as the front button areas do.
[robg adds: I've seen occasional reports of issues with left- and right-button recognition on the Mighty Mouse, but the unit I have here doesn't have such problems.]
Mac OS X Hints