If you use the advanced search tab, you're much more likely to turn up relevant career opportunities. Instead of just searching by the name of the company or person, you can search by keyword, industry, location, and more.
Also, the Companies tab shows you which companies currently have job openings. Click on the Companies tab at the top of your LinkedIn page, then click the second tab, "Search Companies." Then you can search by relevance, or by an advanced keyword search.
It's much more efficient than using the broad job-search feature on LinkedIn.