1. Get the word out.
2. Get LinkedIn recommendations from your colleagues.
3. Find out where people with your backgrounds are working.
4. Find out where people at a company came from.
5. Find out where people from a company go next.
6. Check if a company is still hiring.
7. Get to the hiring manager.
8. Get to the right HR person.
9. Find out the secret job requirements.
10. Find startups to join.
Read Guy's full post for some really good insight. It's one of the best posts I've read about using LinkedIn for a job search.