Learn German: Es ist ein einfach zu korrigierender Fehler. - It is an easily correctable mistake.

This is the Gerundivum. It is formed by combining zu with the present participle of a verb (korrigierend). When placed before a noun like an adjective, it expresses a passive possibility or obligation. Here, it describes a mistake that can be corrected.

Why does the participle take the ending -er here?

Even though it is built from a verb, the entire phrase zu korrigierend acts as an adjective describing the masculine noun Fehler. Because it follows the uninflected indefinite article ein in the nominative case, it must take the strong masculine ending -er.

Why doesn't einfach take an adjective ending like the participle does?

einfach is acting as an adverb here, not an adjective. It does not describe the noun Fehler (it is not a 'simple mistake'), but rather describes the verbal aspect of the phrase, telling us how the mistake can be corrected. Adverbs never take declension endings in German.

The Gerundivum feels quite formal. How would I say this in everyday spoken German?

You are right, this structure is compact and often used in writing. In everyday speech, you would typically unpack it into a relative clause using the verb sein + zu + infinitive: Es ist ein Fehler, der einfach zu korrigieren ist.