With our first adoption homestudy, we were sent a copy and asked to proof-read. I used to do proof-reading and editing as a side-gig, so I read that bad boy cover to cover and marked it up in red. Minor errors, major errors (did they mistake me for somebody else LOL) all got marked up.
When I got my final copy in the mail, I was bummed to see that she had made a few of the edits, but not even all the major errors were corrected. I don't know if I just overwhelmed her or what.
When we got our second homestudy, they didn't send us a proof copy and instead just sent us the final version. There were some errors and some things I felt were a bit misrepresented, but I didn't do anything to have them corrected. I honestly don't think anyone really looked at it all that closely.
That said, it probably depends on the program and the type of errors. Ours were foster adoptions and the errors weren't alarming or problematic in any way.