You leave copies of your fingerprint everywhere, and you can't change it - IMO, if fingerprint was a password, it would be the worst password ever, worse even than 123456. Really the computer equivalent of hitting Enter at the password prompt.

But fingerprints are user IDs, not passwords - so the security-conscious approach would be fingerprint+password; and if screen dirt residue is a concern, use a scrambled keypad. Or just wipe the screen on your shirt :)