Grammatical mistakes?

其實這句可以這樣寫

The agency is hoping (that) the stores will spruce up the system.

而that可以省略，這種句式叫複合句(complex sentence)

複合句是由主要子句＋從屬子句做成，即然是有兩個子句，所以就可以有兩個動詞
句子中The agency is hoping這句是主要子句(Main clause)
而that the store will spruce up the system.是從屬子句(subordinate clause)


希望幫到你！

You can add a verb in future tense after the verb "hope" because it acts as the expectation of someone.

too many verbs=too many subjects
It is not a grammatical mistake.
It is better if you add a comma or
use who/which/that!