The deed is relative to any title claims against the property, that is any ownership right or pledge of the property for a loan (mortgage). The deed should note any easements, rights of way, useage restrictions, etc. also.
A search of the taxing jurisdiction records should tell you if there are any unpaid taxes which could result in the property being sold to satisfy the claim.
Super's comment that utility bills usually go with the person, not the property, is normally the case, however there are exceptions. Any utilities provided by the municipality (often water and sewer; sometime electric and gas) if not paid may be relevied on to the tax bill.