EVERY neuter/spay has those warnings. The number of dogs who actually have issues is very low.
Since you chose to use the ASPCA mobile unit, you had to sign the papers and acknowledge that something could happen in a small % of cases but you accept the risk. They do NOT use incompetent vets for this - they use regular vets who donate their time and supplies to work with the community programs. No, you can't sue.
When you use a vet's clinic for the neuter they have a blood test done prior to surgery to check if the dog's organ function is ok. This stops any problems from exposure to anesthetic or the shock of surgery. With mobile /community programs you do not get the blood test first. That's why it's more expensive at the vets.
You got a competent vet, what you HAD was a problem with the dog going through surgery. Since so much is out of the vet's hands (basic health of the animals they're neuter/spaying, unknown background history, unknown medical problems present) THAT is why you sign the papers first. As an owner you take the risk that your pet may not be 100% able to go through the surgery safely.
You spend $500 in clothes for your dog per week? Honestly? $12,000 a year? And you took the cheap way out to get him neutered?
The low cost programs are for people who have income problems and can't afford to pay full price for vet care.
Neuter/spays are the most common operation done by every vet in the USA. It's safe for 99% of animals that they do it on.
Added-- what I find odd about your post is that you keep referring to 'neutering' and then say you have a female. For males it's neutering - that's surgery on the outside of the body to remove testicles. For females it's SPAYING - which is internal abdominal surgery. It's more extensive and more of a shock to the dog's body. The ovaries and uterus are removed. With males the scrotum gets a 1/2" incision and the testicles are slid out and snipped off - far less shock for the body to absorb.
Small dogs can present issues with abdominal surgery. There are always at least two people in surgery with the pet at all times - the vet doing the proceedure and a vet tech to monitor breathing and heart on the machines. The surgery went however the surgery went. Did you ask questions about what went wrong or did you just yell at everyone?

