There's a lot of info on transmission issues - search for threads and check the e46 wiki link near top of this page.
Just a possibility, but since all these codes popped up after a car wash, I'd suspect water got into some of your connections and caused the error codes. Could mean you have some exposed connectors somewhere. I'd get the mechanic or someone to reset all the codes and then drive it and see what codes come back. Might just need some time to dry out.