Learn German: Ärgert ihr euch über den Fehler? - Are you annoyed about the mistake?

It is the accusative reflexive pronoun for ihr (the informal plural you). The verb sich ärgern (to be annoyed) is a reflexive verb, which means the subject and the pronoun have to match. If you were talking to just one person, it would be Ärgerst du dich.

The English translation doesn't say annoying yourselves. Why is this verb reflexive in German?

Many German verbs that express emotions or feelings are reflexive, even if their English equivalents are not. You can think of sich ärgern as literally meaning to anger oneself, though it simply translates as to be annoyed or to get angry.

Doesn't the preposition über usually mean over or above?

Yes, when talking about a physical location. However, many German verbs are paired with a fixed preposition to express a specific idea. To say you are annoyed about something, German always uses the combination sich ärgern über.

Why is it den Fehler (accusative) instead of der Fehler?

When the preposition über is used figuratively as a fixed pair with a verb like sich ärgern, it always forces the noun that follows into the accusative case. Since Fehler (mistake) is a masculine noun, its article changes from der to den.