Previous owner didn't get permits for remodel, am I now liable?
Sorry, I am going to have to disagree with some of the above posters.  It all comes down to the interpretation of due diligence.  

Hypothetically, if you bought the place and know that work was done without permits, you have actually created your own problem, now, by advertising the fact that you know about the negligent work.  If you now rent it and there is a problem, you could be civilly liable (you could be liable for replacing a tenants possessions if there is a flood from a faulty pipe) or criminally liable (a faulty wire burns down the house and kills someone).  I can tell you of at least 7 instances of people we have done work for that their insurance didn't cover their repairs after problems.  It is usually when they have work done without permits and it creates a flood or a fire, but the legal logic is the same.

The very fact you know about it implies you have a moral obligation to repair the faults you know of prior to acting as a landlord.  The fact that you just put it out on the internet makes it vital.  As unlikely as it seems that a future possible catastrophe could be linked back to this post and you (your profile says Jim Garrison of Austin, TX - there are only 19 people with your name in Austin - see how easy it would be?), do you really want to take that risk?

You would be wisest to have the work inspected by a competent whoever (don't know the work done) and inform your insurance company of it in writing.  Also talk to the town and get an inspection by the town done.  If you can pull a permit and have them check it, you will be pretty safe.  Just get them to put it in writing that it passes.  Do not accept a private home inspectors report as anything.  They simply don't hold up in court, and I have seen that in multiple instances.

Good luck.