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It's not always easy to differentiate general font problems from those caused by Font Book (see Laying the Blame for help with that)—which means it's not all that clear what you should do about them, either.
If you're convinced that you have a Font Book problem but can't pinpoint it, read the solutions for nonspecific problems that follow immediately after this list of links. If you can pinpoint the problem a little—it seems connected to user-defined libraries, say, or the dots that mark duplicate fonts don't seem to make sense—try the appropriate link from the list.