In addition to discussing their facility (how many stalls, how often they're stripped, how much shavings are used, feed, turn out), equipment (walkers, treadmills, pools), experience and training philosophies, I discuss how they feel about drugging horses for shows, disciplining horses, harsh methods of training, equipment they'll use or not and why.
Back when I first started showing I had a gelding and never had a CLUE that horses were routinely given Regumate in both mares & stallions to make them easier to handle. Never knew that some trainers routinely inject ACTH, Bute and other NSAIDS at shows without discussing it with the owner. Now that I've been showing mares and stallions, and I know this goes on, I discuss it with a potential trainer and I let them know that it's not acceptable. I NEVER allow their hormones to be messed with for any reason not related to therapeutic treatment prescribed by a vet for use in the breeding shed.
I also don't allow Bute and Banamine to be given just because a horse has to stand in a stall at a show. I do have rubber mats to put down under the shavings, and I will happily bed my own horses stall if the trainer feels they can't be bothered with the mats, but that's really not been a problem because we discuss it FIRST before they get the horse and they've agreed that they're ok doing this my way.
Discipline is another topic of discussion. Spank 'em with a crop if they need it, reach out and touch 'em with the lunge whip if they've earned it and are being piggish. But Belly Kicking and Ear Twisting, or Hot Shotting will get my horse pulled out of the barn in a hot second. I know other folks are ok with it, I'm not and since it's my checkbook, I either get my way on this or we find another trainer.
Since my horses generally get sent out of state for training, it's imperative to me to feel like I can trust the trainer to honor my wishes. So if it's a new trainer that I've never used before, I make the trip by myself first and check out their situation and watch them train horses and give a few lessons, in addition to talking about my hot buttons.
Oh, another topic that came up unexpectedly. The trainer who does a lovely job training your horse but refused to allow you to touch him. SAY WHAT? I found a trainer that I just love, and love how he trains his horses. BUT, he wants to do all the riding and showing, and even when I told him that he would NOT be doing all the riding and showing, didn't want me to ride my own horses. Needless to say, the horses aren't in his barn anylonger.
So my point is, I think we could all have fewer problems when boarding and training if we'd open up the lines of communication BEFORE there's a problem. I rarely have to say anything about my horses' treatment or care at the trainer's because they know BEFORE they even think about doing something if it's a problem or not, or they know to ask before they do it to make sure if they have a doubt.