I'm pretty sure Limewire is adware, but prolly not spyware. Spyware typically runs all the time recording stuff on your computer to be sent back to the HQ or something. Adware are the banner advertisements in the limewire app itself. If you have spyware on the Mac, I believe it'd be pointed out when you boot (the loading window showing stuff starting up) or definitely be present in you process window once logged in. Either was, I'm sure spyware would require a root password to install to be able to work properly.
This is why I hate that in 10.3.2 that any app can change system level files with only a password. Before, if I'm correct, to change something in root owned folders one had to sudo in terminal, which IMO, is a lot securer.