We had a retired racer for 10 years. Please remember, even dogs of the same breeds can vary wildly. However, a nickname for greyhounds is “the worlds fastest couch potato.” They live up to it quite well. Ours had his own couch.
They are great pets, but try not to think of them like dogs. First off, it is virtually impossible for a greyhound to sit, especially retired racers, their thigh muscles are just too darn big. Ours was never able to. Playing for them is running full tilt or sleeping. They don’t catch, they don’t fetch, they don’t really do tricks. However, a retired racer is extremely used to being handled by many different people. Ours would stand around while the neighborhood kids swarmed him. We also had a cat that Critic didn’t care two hoots about.
Sight hounds-that is what they are. What is a speck in the distance to you, is a short run for them. When your greyhound escapes, you get the car, you don’t walk. I will say that I worked for a few weeks to teach ours the perimeter of our yard and he kept to it quite well. They are not impossible to train that way, it just takes work. They, as racers, don’t get a lot of playtime off leash.
Also, be aware, not all “rescue” greyhounds are retired racers. The more squirrely ones I have witnessed (darn few I might add) were never racers. Not every dog races and the rescue groups take pretty much all of them. I definitely would select a retired racer due to their ease at being handled.
These racers are not disposable. They are what make the kennel owners money. You don’t abuse your money maker, if you do, you are stupid. You should see the greyhound whirlpool. It isn’t living in a mansion, but by and large, they are treated very well when they are racing. The problems typically occur when the dogs stop racing and aren’t good enough to breed. It is not necessary to consider them all abused by any stretch of the imagination.
Bleeding: Greyhounds bleed easily. Any cut or scrape can bleed prolifically. They have extremely thin skin, as a matter of fact, many vets keep them around as blood donors, nice fat veins, easy to reach and thin skin. WOOT! We clipped ours nails once and by the time we got back around to the front, there was a puddle of blood around his foot. Ooopsie!
Diet: Ours may have had a lifetime problem with his digestion, but he had the most sensitive stomach I’ve ever seen. He was quite prone to diarrhea. Generally, you always have a bag of rice in the house to help settle their stomachs. I seem to recall giving him pepto bismol too. (He ended up dying as a result of an intestinal blockage. His intestines were basically a knot. He was always thin, even for a greyhound, and by the time we realized it wasn’t worms or something easy, he was of too low a weight to risk exploratory surgery, it was most probably a congenital problem.)
Beds: They have bones everywhere and they are quite large, where a regular dog can be ok just on a rug or on a bare floor, really, a greyhound needs a bit more cushion than that. They can be quite the bed hog, fair warning. 
Just please remember, if you want a doggy dog, they aren’t it. What they are are very sweet, lovable, gentle, peaceful animals. Really, an apartment is ok with them, as long as you walk them. Ours was quite happy to retire, thankyouverymuch.
Also, many of the rescue groups are batshit crazy. They take things to the nth degree. I kind of understand, but sometimes it seems like they would rather keep the dogs themselves than let them get adopted. They are extraordinarily easy dogs to like to have around.
I would gladly have a herd of them. I think they are phenomenal. I miss ours even now and he’s been gone about 8 years. I would recommend them to anyone, of any age, as long as they understood the facts about their temperaments.
======end of greyhound owner====
------begin greyhound track employee-----
I never saw the kennels but was friends with a girl that worked in them for about 10 years. She hates the reputations that greyhound breeders have. She would tell me about staying there for days on end because one of her dogs was sick, about how much she loved the dogs and what it was like taking care of them. In the 4 years I worked at the track, I’d never seen or heard of any form of abuse or neglect. Dogs get hurt when they race, it happens and when it is bad, it is horrible to see, but by and large, it is a rare occurance, although I know that toe dislocations are quite common because they always turn on their left side. I knew several kennel owners who all seemed to be pretty upright folks. Our track used to have the adoption center on site, but the organization no longer does that. When the adoption folks bring dogs, I’ve never known them to bring adoptable dogs. They bring their pets, which I think is a disservice. It is one more hoop they make you jump through to getting one. While I loved visiting with the rescue dogs, I kept my mouth shut otherwise.
Example: they required us to purchase a large crate as a condition of adoption. Our dog hated it and refused to ever go in it.
These dogs need good homes. There is no shortage of greyhounds, just a shortage of homes. Once you experience having one, the urge to get more is quite profound. They really are just super nice dogs. I think we are the only people we knew that only had one. Well, we got an italian greyhound, they were a funny pair.