A potential downside of fingerprint-recognition systems is their novelty. I've seen casual passersby stop and touch the finger platen to see if their fingerprint can fool the system. I don't know of any successful attempts yet, but you typically wouldn't have the same level of interest in trying to guess someone's password. In time, the novelty will surely wear off. A big variable among manufacturers is the maximum allowable finger displacement and finger rotation relative to the fingerprint used in training.
Sensors are also fairly sensitive to mangled or otherwise disguised fingerprints.
Of course, any form of biometric security can be defeated, given enough determination. For example, your fingerprint scanning results are stored on some computer, and a sufficiently motivated hacker could simply steal the file. In general, your data are probably secure, but a little insurance never hurts. By taking a few precautions, investing in a few key technologies, and using a modicum of common sense, you can protect your valuable information from most everyday situations. Simply identify the level of risk you're willing to live with and how much you're willing to spend in time and resources to achieve that comfort level.