One of the most common mistakes made when using objective pronouns is when using the compound subject you and me. Because you is the same in the subjective and the objective case, people get confused between I and me. The way to check this is to remove the second-person pronoun.
When he’s finished reading the book, he’ll give it to you or I.
If the sentence read “…he’ll give it to I”, we would know it was wrong. We could also look for the preposition: or.
When he’s finished reading the book, he’ll give it to you or me.