When a user is forwarding inline a PGP/MIME-signed message, there's absolutely no point to retain the application/pgp-signature attachment, because the original bits of the original message aren't preserved anyway. The attachment should be removed. Actually, leaving that attachment only causes additional problems. For example, if I forward inline and PGP/MIME sign a PGP/MIME-signed message, it seems to confuse the recieving UA (my own Tb with Enigmail in this case), so the UA silently ignores the presence of the signature, again showing just an attachment named signature.asc instead.
Works for me in Thunderbird 11.0.1. The "signature.asc" attachment is not included when forwarding inline. Perhaps this bug can be marked as FIXED.
I think I can still reproduce the problem on Tb12. Presence of the signature is not indicated in any way when showing the message, but if I click on Forward, I see signature.asc in the list of attachments.