I have a tenant who moved in without ever signing a lease, should I be legally concerned of my exposure, or does it really matter?The building is...

As a general rule, if there is no written lease, the
tenant occupies the premises only as a tenacy at will which may be terminated by the
Landlord upon notice. Since leases involve real estate, any contract or transaction
involving real estate should be in writing to avoid violation of the Statute of Frauds.
It would appear in this instance that your tenant has no legal right to occupy the
premises without your express permission and that you would be legally entitled to begin
eviction proceedings.

Having said that, please note I have
emphasized that this is a "general rule." It is entirely
possible that there are state or local statutes which provide exceptions to the rule.
You would be well advised to consult a local attorney for more specific guidance. "Free"
legal advice is worth what you pay for it.