As far as I know the hotspot for any physics object needs to be centered in order for the collision to work properly. If I remember correctly this has something to do with the way Box2D works.
If you need the hotspot at the edge of the flipper for whatever reason then make your sprite like so:
<img src="http://i45.tinypic.com/i6clc9.png">
Then when you draw your custom collision mask in the layout, just place your points around the colored area like normal.
1 ) How do you increase the accuracy of the physics.
It's hard to say without a .cap to look at to see what's wrong.
2 ) Are there issues with physics objects and mouse control? Again, seems flakey for me when I use it
Yes. If you manually move a physics object with the mouse or a behavior or by updating it's coordinates in any way except with physics itself, then you will get weird collisions. Also, when you manually move the flipper against the ball with the mouse, the flipper has no force, so it's not actually "hitting" the ball. You're just intersecting the flipper and the ball. The ball and the flipper are trying to push out of each other, but the mouse behavior is overriding it's position.
Here's a method for moving physics object around with the mouse that may suit your needs:
http://dl.dropbox.com/u/529356/dragandtoss.cap
It's got a little bit of lag behind the mouse but it works pretty well.