I haven't even updated my iphone to 2.01 yet and I just started to have those problems with my mail. Safari is still good. A coworker said that I should update my phone. So apparently he isn't having problems with the current update.
Not sure about the phone, but as for my iPod Touch, everything worked well except for the DNS issue with wifi until I updated to 2.0, 2.0.1, and 2.0.2 - now I hate my iPod. Nothing works except wifi
edit- fixed spelling errors