Look for healthy, happy horses that want to come to you when you are walking around the property. The behavior of the horses on the property can tell you a lot about how they are being treated.
Find out what type of riding the majority of the riders do and the general age range - most adult trail riders don't want to board with a barnful of show-crazy tweens....or vice versa.
If there is something you are looking for in terms of riding or training opportunities - make sure you'll have what you need (an instructor in your discipline, lots of trails, whatever).
Good fences. Clean stalls. A living arrangement your horse can live with (enough room in pasture, not overcrowded, stalls if your horse needs them, etc).
Talk to the boarders. Talk to your vet or local tack store/feed store owners. Just ask around.
Also, about the penicillin screw up - sadly, those things do happen. I wouldn't necessarily say it was a bad barn due to the accident - but I wouldn't let the owner provide any veterinary care to my horse. Please remember that the vast majority of barn owners/managers do give shots, first aid treatment etc - but are not trained professionals in terms of veterinary medicine and should NOT be regarded as such by you unless they have some professional credentials to go with it. I don't discredit experience, but I always cringe when I see people taking a trainer or BO's advice on meds instead of calling a vet or following their vet's advice.