Facebook may be close to putting a Federal Trade Commission investigation behind it. But it faces a variety of other probes in Europe and the U.S., some of which could present it with even bigger headaches.

While the $5 billion fine from the FTC, which Facebook has been expecting, is by far the largest the agency has levied on a technology company, the real worries for Facebook — and its investors and the companies that use it to advertise on its service — are the other restrictions and government oversight that might come with it. This goes for the other investigations as well, which span the...