I'm not an expert but I'd look for any metal fatigue inside the firebox, or if there is stone inside the firebox I'd look for cracking or spalling, signs of degredation. I'd examine the outside closely to see if there are any signs of smoke residue where it shouldn't be, especially at the joints, or cracks in the stones or seams. Make sure all handles and flaps for the flue and air supply are working or repairable, door hinges and latches working and tight.
Things like fiberglass gaskets on the doors can easily be replaced, other items might have to be custom built.
It looks like a beautiful stove, I'd look at the cost vs. my bank statement vs. my dwelling size.
I'd also look at the stove they replaced it with, if it looks like it has a higher output I'd be suspicious, maybe it doesn't put out as much heat as they are suggesting or maybe it isn't efficient
enough.
I'd look at the calendar before I make a counter offer, Spring favors a buyer for a woodstove.
Then I'd probably look for my 3 biggest friends to help me carry it out of the basement, it looks heavy.