Hi I don't think it's possible.
As of mysql 5.1.29 - you can specify storage option (table or file) and location and which log you want - error, general, binary or slow query. As far as I know - you can't specify format of the log or what gets logged. I might be wrong - but I think that all login attemps will be logged in general log, and not the error one.
However, assuming your mysql server is running on a separate machine, from you applicaiton server, and you need port 3306 ( or whatever) open and you can't use ssh tunnel, you mysql server still shouldn't be accessible by anyone willy-nilly. I highly recommend not to expose it to web traffic, and if you must ( like in case of the residing somewhere not behind your firewall) bind it to the ip address or ip block of you application server and your admin access ip ( where you are accessing from)
Hope that helps.