Learn Russian: Мы считаем этот муниципальный проект ошибкой мэра. - We consider this municipal project the mayor's mistake.

The verb считать (to consider) takes a direct object in the Accusative (этот муниципальный проект) and describes what it is considered to be using the Instrumental (ошибкой). This is the standard pattern for Russian verbs of considering, naming, and appointing.

Isn't этот муниципальный проект the direct object? Why does it look like it's in the Nominative case?

It is indeed the direct object and is in the Accusative case. Because проект is an inanimate masculine noun, its Accusative form is exactly the same as its Nominative form. The pronoun этот and adjective муниципальный agree with it and also take the inanimate Accusative form.

Doesn't the verb считать mean "to count"?

Yes, its literal meaning is "to count" (like counting numbers). But just like the English phrase "I count him as a friend," считать is heavily used to mean "to consider" or "to hold an opinion."

Why is мэра in the Genitive case? Does it connect to the verb?

No, мэра doesn't connect to the verb at all. It is in the Genitive case because it modifies the noun ошибкой, showing possession. It literally translates to "a mistake of the mayor."