In addition to many and much, there are a number of other quantifiers that can only be used with either countable or uncountable nouns. Simplifying the facts somewhat, most of these alternative quantifiers are mainly used instead of many and much for the sake of variation. So, instead of (1), people often use, for instance, (2), (3), (4), (5), or (6):
(1) We have discovered many problematic areas.
(2) We have discovered quite a few problematic areas.
(3) We have discovered quite a large number of problematic areas.
(4) We have discovered numerous problematic areas.
(5) We have discovered a great many problematic areas.
(6) We have discovered several problematic areas.
It would certainly be interesting to investigate the intuitions that native speakers have about these quantifiers and the quantities that they represent.
A similar situation holds for uncountable nouns and the quantifiers that are used with those. Instead of (7), people will thus often choose to use, inter alia, (8), (9), or (10) instead:
(7) Our new project will cost much money.
(8) Our new project will cost a great deal of money.
(9) Our new project will cost large amounts of money.
(10) Our new project will cost a large amount of money.