Learn Italian: Credo che appendere il manifesto lì sia un errore. - I believe that hanging the poster there is a mistake.

You are correct that when believing a noun or a person, Italian uses credere a (like credo a Marco for 'I believe Marco'). However, as this lesson covers, when a verb that normally takes a is followed by the declarative conjunction che to introduce a new clause, the preposition is mandatorily deleted. Saying credo a che is incorrect, so it simply becomes credo che.

Why is sia in the subjunctive mood rather than the indicative è?

Verbs expressing opinion, belief, or uncertainty like credere (to believe) trigger the subjunctive mood in the following che clause. Since the speaker is expressing a subjective opinion rather than stating an objective fact, the present subjunctive sia is required instead of the indicative è.

Why is the infinitive appendere used here to mean 'hanging'?

In Italian, the infinitive acts as a verbal noun. Whenever an action itself is the subject of a clause (here, the act of hanging the poster), you must use the infinitive. English often uses an '-ing' gerund for this purpose, but Italian never uses its own -ndo gerund forms as subjects.

Why does lì have an accent mark?