Disable your MagicPrefs - it's in the magicPrefs menu.
Open your System Prefs/Mouse pane
Change "Secondary click" to left.
That reverses right and left clicks.
Now, Left-click will show contextual menus, and right-click selects or double-clicks
Do you get the same response from the Magic Mouse?
Especially try the (now) right click to double-click on something. Is the right side still very difficult to get response?
As fryke suggested, the right-click will not work properly if you are inadvertently touching the mouse with any other finger or other part of your hand.
Be sure to change your secondary click back to "right". Gets really confusing (at least for me
)
The MagicPrefs (and other utilities) will allow a lot of other adjustments to what your Magic Mouse can do. You can see there's several zones on the top surface of the mouse that can be used for other purposes, or just turned off (which can leave you with 'dead' zones - the area around the Apple symbol is one of those)
Take some time to see what changes you can make with MagicPrefs. The interesting one is where you can move the cursor directly from the surface of the Magic Mouse (without moving the mouse at all, eh?)