Sixfootdwarf
To determine whether someone has been downloading illegal material you will need a computer forensic expert but these people are quite expensive but I believe they have the necessary utilities/tools needed to tell you, with any kind of certainty, what someone has been up to with their PC.
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to the best of my knowledge its not possible for limewire to say it is downloading something with out some sat in front of the computer.
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That is correct unless that PC has been infected by a virus or worm.
However, it is unlikely that a virus, worm or whatever would put anything into the "Incomplete" folder, any malware would deposit files in the "Shared" folder in order to stand a better chance of spreading to other user's PCs.
Finally, to make sure that this individual's HD is not infected with something that may be planting rubbish on his PC you should run an AV, Ewido anti-spyware along with Adware SE and Spybot. If they all come up clean then it is more than likely that this person may have been downloading stuff his partner finds objectionable.
UK Bob
PS. I must admit that I find this kind of investigation somewhat distasteful, if one partner has problems with the other then they should sort their problems out between themselves. Calling in a third party, unless absolutely necessary, seems to be all wrong.