Suggested answer:
(1)
The following forms have been used incorrectly according to grammatical rules for standard English: quick, slow, quicker, and slower.
Examples:
"I'd need the cash pretty quick ...
And as I felt that it came quicker and ...
...they tend to run either fast or slow ...
I felt distinguished, and looked more melancholy, and walked slower.

(2) The examples above show incorrect/substandard usage in the sense that an adjective form has been used in contexts where an adverb/adverb phrase is required. The adjectives have been incorrectly used to modify verbs; only adverbs can modify verbs.

(3) We expect to find substandard usage of this kind in formal language. In the corpus, we typically find this kind of error in film dialogue, direct speech, including slang.

---

Read about the use of adjectives vs. adverbs here.
Read about standard use of comparative forms of adjectives and adverbs here (Rule 6).
Terminology: adjective, adverb, and comparative.