Without accurate WHOIS info you face a big problem. I have had success tracking those people down (but i had to WORK for it). These ideas are geared towards inaccurate and not private registration (save the first one which applies to both):
1. You can place a backorder and wait until the domain expires to snatch it up. Google how to do this effectively because you aren't the only one who is after that domain.
2. Search for the whois email in the search engines to see if you can find any sites that have that email on them. Go through each site and do some investigating and you might get lucky by finding their profile somewhere. Use any alternate forms of contact you find. Repeat this step with each form of contact that you find.
3. Use location information from the whois and whatever names they have there and look up old phone records. i.e. If they gave you st. paul, alberta canada and only part of their name you would find the phonebook (call the local phone companies in the area...they sometimes have old ones that they are happy to mail) that was published just after the domain was registered and go down the list calling each potential match. This works if they typed their phone number wrong.
4. Go to the domain you are after and have a look at the website. If it is a standard template looking thing then you can run some of the words on the page through copyscape.com and see any other domains he has registered. Also try googling those phrases as well. This one is hit or miss.
5. Submit a whois complaint: http://wdprs.internic.net/
Hope this helps!
Jason Jackson