First of all, each of the examples given in the body of your question should be "whom."
This is a holdover from when the English language had cases, which you sort of referenced by noting the difficulty in identifying a subject. Who is always a subject, while whom is either a direct object, indirect object, or object of preposition:
1) Whom did you kill? (DO)
2) To whom did you give the book? (IO)
3) Who is the person about whom you are talking? (ObjP)
If it is difficult to tell by looking at the original sentence, try moving the who/whom in the sentence to see whether it holds an object position:
1) ...the Government has instructed Heads of Department to terminate whom from long-standing provisional employment.
2)...the Supervising Teacher considered whom deserving of compensatory remuneration...
3)...the academic committee had originally advised against whom...
4)...she had expressed reservations about whom in writing...
5)...the Supervising Teacher had specifically shown a reluctance towards nominating whom...
It may initially feel weird performing this kind of move operation, but if you can't immediately see whether the who/whom is acting as an object or not, then this is the easiest way to disambiguate that.
Best Answer
Yes, you probably are losing your mind. :)
I say that (in jest!) because there is no grammatical or spelling mistake in this sentence:
Depending on the writing assignment, they may wish it rewritten for any number of reasons, but the spelling and grammar are still ok.
They might conceivably want something like these:
But those are all just elaborating and rewriting to emphasize different aspects of the thought they wish to convey. They are no better in terms of grammar or spelling than your original.
John Lawler in comments points out two possible things they might be thinking are wrong.
So one is that many is of a different, less casual register than a lot of.
Those are more casual than the original, but mean the same thing.
The other issue John raises is that they might be thinking that many is automatically limited to negative contexts only, such as:
However many isn’t so limited. It may also not be true. :)
There are places where many can only be used as a negative polarity item, but this is not one of them. See Professor Lawler’s NPI cheat-sheet.
If you wanted a version of your original that did have an error in grammar or spelling, then any of these would do:
One thing that would not be an error is the who. You can say who there just like you can say that (some people might even try to say which), but that doesn’t change anything.