Go back and take a look at your original lease. I'm pretty sure there will be language about "patent defects vs latent defects". The air conditioner claim may have merit if you took responsibility for reporting any problems with mechanical devices and failed to have it repaired or if there is a problem attributable to your own neglect. That would be a latent defect (one that could not reasonably be found during the "walk through").
I'm always of the opinion that you at least try and resolve the issue before "taking the fight to them". These other guys are telling you to lawyer up, go to court, etc. So if you hire a lawyer for $500-1000 to defend you and spend 3-4 hours over two nights in court (because you know damn well it won't get resolved in one night) you are out $1000 and your own time. On the other hand, you could call her or her attorney and offer to pay her $300 to get the air conditioner fixed and send her the check in 15 minutes for the cost of a postage stamp.
I guess I always look at things (in my personal life) from the perspective of how much time out of my life will this take to resolve and go with the quickest route.