I'd certainly start by taking pictures and having double-copies of them made to send along in a certified letter, return receipt requested envelope along with a letter of your intentions to 'monitor' the situation. I'm not a lawyer but I think you have 2 ways to go about it.
First, find out what the 'limit' is on how long you can wait to file a suit (should it come to that.) IF it comes to filing suit, and you don't see any damage other than the 'looks', then you need to ask yourself: Is it worth my $$$ and time to persue a suit? If the answer is YES, the you do it. If the answer is NO, then you 'live' with it.
Second, consult that Arborist and ask about the damage. Thing is, you don't know if he 'dumped' his thinner on the lawn or something. The Arborist might suggest you try 'scraping' a little on the top layer to remove some of the obvious paint. (Then again, he may not.) Bottom line is: If this turns out to only be an 'aestetic' problem, can you live with it?
Yes, I'd be upset too. But as a judge, what would you want the Painter to 'compensate' you for? Sure, there's paint on the tree but if it's alive and thriving, he may end up killing the tree in an attempt to clean it. So, as I see it from here, it's a tough 'situation' with some tough 'decisions'. I did give this some thought but I'm truely at a loss as to what he should 'compensate' me for. Again, I'm not sure I'd let him clean the tree because he may kill it. Maybe you do need to talk to a lawyer. I guess at worst, you don't recommend him to anyone and you file a complaint with the BBB.
As for the bark, its purpose is to protect the tree. That's why I don't think it would be too much of a problem to 'scrape' off the paint from the tree a little. But do talk to an Arborist first. Maybe you can sue him for that Fee, and so on. I wish I knew what, exactly, you should do. My best to ya and hope this helps.