Learn Croatian: Mnogi posjetitelji traže nova izdanja. - Many visitors are looking for new editions.

Mnogi is an adjective that changes its endings to match the noun it describes. Here, it matches the nominative masculine plural noun posjetitelji. If you used mnogo, it would act as a fixed quantity word and force the noun into the genitive case, which would be mnogo posjetitelja.

What case is nova izdanja in, and why?

It is in the accusative case because it is the direct object of the verb traže (are looking for). Izdanje (edition) is a neuter noun. For neuter nouns in the plural, the accusative and nominative forms are identical, ending in -a.

Could we say traže za nova izdanja to mean "looking for new editions"?

No, in Croatian you do not use a preposition like za for "looking for". The verb tražiti inherently means "to look for" or "to seek" all on its own, and it directly takes an object in the accusative case.

How is the word posjetitelji formed?

It comes from the verb posjetiti (to visit). Adding the suffix -elj is a common way to turn a verb into a noun that represents a person doing that action, resulting in posjetitelj (visitor). Here it is in the nominative plural form.