I really don't see much in your log. Have you followed all the steps HERE?
If you have not then I would advise you to do so and see if that makes a difference.
When you say the mouse is erratic exactly what do you mean? Have you cleaned the mouse? Sometimes a build up of dust can cause the mouse to behave erratically.

Unplug the mouse from the computer.

Remove the cover from the bottom of the mouse and remove the ball. Use something like a soft tissue to clean off any dust or debris from the ball itself.
Next, notice the 3 rollers within the mouse casing, these are what we need to clean.

You can improvise on how to clean the rollers, using your fingernail gets good results, if the mouse hasn't been cleaned before then you will see lots of dust on the rollers, whichever way you choose to clean them make sure you remove all traces of dust/debris as the smallest piece can cause the mouse to behave erratically.

When you have removed all traces of dust/dirt from the rollers and the ball is nice and clean, simply put the ball back in and replace the cover turning clockwise to lock it in place.

Plug the mouse back into your machine and turn the machine on, now your mouse should be as good as new.