I agree this is not good and if there was a nick the groomer should've told you what happend and I can see how this accident may of happened, especially if he was clipper cut.
Being a Sheepdog X Chow Chow I can imagine this dog has a VERY dense coat and clipping this coat can be tricky. Seeing as you asked it to be short, but not shaved I'll assume his body was done with a comb attatchment, his genitalia clipped shorter and his feet neatened with clippers.
The skin can be quite loose around the sanitary area and in order to clip around there you need to pull the skin taught. Faliure to do that may cause the skin to feed into the clipper and become nicked and thats how this may of happened. Same with his feet, if they were trimmed using clippers the foot wasn't listed and positioned flat so the skin prob fed through the clipper.
May I ask, how bad are the nicks and am I right with what he recieved at the groomers?
this will help in determining how he got them and how to make your little boy better again
cut by the groomer 
for dogs that you could put on the irritated/nicked areas to make him feel better and keep it from getting infected. 
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