If you happen to spot a mistake, let me know immediately.

Literal

By-chance mistake [object-を] find-[conditional-たら], immediately inform-[polite request-てください].

直ちに ('immediately, at once') is a formal adverb, more emphatic than すぐに. It carries an imperative urgency often found in official notices or rules. 見つける ('to find') is the transitive counterpart of 見つかる ('to be found').