Translation:I made a lot of mistakes in the examination.
Is "lots of" a missing alternative or is it really wrong?
Bence doğru - it sounds correct to me.
why not hataları?
Because "çok" takes the singular, and because indefinite objects don't (usually) take the plural suffix -- see https://www.duolingo.com/comment/7736911 .
Even that is correct.
I answered, " I made several mistakes in the exam, " and it was marked wrong. What's the preferred word for several, then?
how come a and mistakes
"a lot" is singular, so it takes the singular article "a".
you make lots of mistakes or a mistake