I finally managed to test
Jaksta for Mac again.
After installing it on Mac OS X 10.6.2, I had problems detecting stream URLs. I rebooted Mac and got much better results. All songs from Grooveshark were detected properly. I didn't have to clean the cache of my browser even when recording songs that had been played before. Tried the latest Firefox as well as Safari. Didn't notice any difference.
The only problem I had is that some songs were not renamed and tagged automatically. But this is a limitation of the song identification service used by Jaksta.
To solve your problem, the developer will probably need your log file. To create it, you need to go to Jaksta -> Preferences... -> Check "Enable Debug mode". Then start monitoring, go to web-sites you have problems with, then send the log to the developer.