I would have to research the facility very carefully. I might have been more open to it until I toured a medical school anatomy lab as part of Medical Explorers. That is the only time I have seen bodies that were donated, but they were treated with absolutely no respect. People's organs had been lost and one body had been left out in the open until it dried up (and no, not on purpose). I truly hope this was the exception and not the rule, but after seeing that I would really have to look hard at any place before I would be comfortable with my loved one donating. Yes, they're done with their bodies, but they still need to be treated with respect.
I can't speak for the place that you saw, but generally, things that go on in anatomy labs can seem shocking to the people that just aren't used to it. I don't know when you visited, but generally, by the end of the year, all the cadavers will be dried out, no matter how much you spray them. And it could be that a few students were just there, stepped out, and were coming right back.
As for organs being lost, I doubt that's true either. It's kind of hard to lose an organ. Yes, they will be removed, but every anatomy lab has a container under each table where you put anything you've taken out so that it gets cremated and returned to the right family, so that it's only that person's remains going and nothing else. I know in our anatomy lab, the professors would do random checks of our buckets to be sure that nothing else was in there. I remember once, somebody must have cut their glove and not noticed that a piece of it fell into the bucket. One of the professors saw the blue of the glove, and completely flipped out, made that group go through the entire bucket to be sure nothing else wasn't there that didn't belong. Once it's full, you bring the container to the lab coordinator who puts it in a bigger container, and you bring your empty one back to your table. So it probably wasn't lost, just in holding somewhere.
I personally didn't see anybody ever disrespecting a body. Sure, we may have joked about some of the more interesting tattoos, or certain implants one of the gentlemen had, pretty much every group named their cadaver. Yes, people would complain in the beginning about the insane amount of fat that some of them had, and at the end, those with skinny bodies were complainign about how dried out they were, but it's nothing bad. You can't expect people to be serious and solemn the entire time. I remember when we were dissecting the hand, our lady had some nasty arthritis when she was alive, and her entire hand was all contracted, and we couldn't get to the fingers. So our professor decided we should just cut one of the tendons to free up one of the fingers so we could dissect it. Didn't realize at the time, but realized it pretty much right away afterwards. For the rest of the year, our lovely lady was flipping the bird to everybody that walked past

We all joked about it, laughed about Millie having an attitude, but it's not in a disrespectful way. Just because it really was quite amusing, and because it's such an abnormal experience, you do what you can to get through it, even if it means joking around.
Maybe our lab was an exception, I really don't know, I've only ever seen the way things work in my lab class. But I imagine that it would be pretty much the same everywhere else. It's a bit morbid to think about, especially if you're donating to a med school because you know that every part of your body will be dissected. But it really is a beautiful gift, and I guarantee you that nobody will say anatomy is a waste of time. OK fine, there's' an argument as to whether doing the actual dissection is helpful, but being able to see how everything fits together in 3D is really very important.