my roommate and I were recently charged for holes burned in the back of our couch from the heater in our furnished apartment. The couch was already placed in front of the heater when we moved in, but we failed to search behind the couch when we moved in. Months later we moved the couch to increase the air flow for the heater and discovered the burns. We never smelled or noticed anything burning. Now when we moved out they are charging us for the burns. Do we have any right to argue or do we take the blame and pay?

if you have no proof they were there prior then yes they can charge you

That's a tough one since it was not reported when you first moved in. My opinion is to write a letter stating the damage was done when you moved in. If you end up going to court over it then pretty much it's your word against theirs. GOOD LUCK!