All tags {JFBClogin} do not work

Check and see if you've added a "Social Tag Admin Key" to the JFBConnect Social configuration area in the Misc tab. If you have a key there, then the tag should be:
{JFBCLogin key=xxxx} (xxxx = whatever your key is)

The key prevents users on your site from adding tags, which could be bad.

If that doesn't work, and although it should be case-insensitive, try it with a capital L, {JFBCLogin}

Let us know if any of the above helps!