You should be OK if you've cleared it with AdAware. just make asure that you run it regularly and keep it up to date. These Spyware things come along in quite legit. programs as well as dodgy ones and it isn't really the function of a firewall to protect against them.
As long as you have a good anti-virus, a good firewall and a good spyware catcher you should be OK until some berk comes along with some new nasty to inflict on us. You might consider putting SpywareBlaster in as this keeps tabs on everything coming it and prevents spy stuff getting in your machine.
With all these things, it is vital to keep them up to date.