To add to barts list of practical things, here's some legal things:
-Make sure there is not some 'management out' clause in the lease (meaning that the "landlord/owner can end this agreement at any time"). You want to make sure whoever is in charge of the place is held accountable to the lease just as much as you are.
-Terin mentioned Renters Insurance - first find out how liable you are in the case of a fire or other incident... many apartments are already insured, and if they are, you need to know the conditions under which the unit is covered.
-When you sign the lease, make ABSOLUTELY sure the management signs and copies the agreement for you. Save this agreement in a protected place. Almost every place I've tried to rent has tried to sucker me out of a copy of the lease or give me an unsigned copy - this will not be sufficient in case you need to go to court (just a precaution).
-Make sure you record every spec of damage or dirt in the unit when you move in - a digital photo with a date stamp will do it. This protects you from them stealing your security deposit (which all landlords try to do)
--Make sure the lease has no unreasonable auto-renewal clause.
There are tons and tons of cases as precedent to challenge pretty much any auto-renewal clauses, and any landlord that adds that is just asking for a lawsuit.
I hope this helps, the law office I was a clerk at had a partner who specialized in Landlord/Tenant law, so I picked up some. Other than that, just use common sense - if it's too good to be true, it is.