In the final episode of Firefly, the bounty hunter Early indicates Book is not a Shepherd. Is there any in-universe explanation for this claim?
Whedon has previously stated that one of Early's key abilities is to quickly evaluate people - he sees in Book attributes not often present in a Shepherd (effectively a pastor), but rather those of his past as a double-agent officer in the Alliance (see What was Shepherd Book's past in Firefly? and the graphic novel @MPelletier references for some details).
The best explanation would be in The Shepherd's Tale, the comic book that came out in 2010. While Early is not encountered, it is clear that Book has had a tumultuous past.
Jubal Early is outting a former Alliance agent, Book, who, as Early will later, comes out of a crisis of faith with a new outlook. And in Book's case, new faith. We don't know how Early will come out of it...
The first evidence of this is in one of the episodes, the one where Book gets medical treatment for one of the crew on an Alliance starship simply by showing his ID.
Early, by the way, isn't a bounty hunter. He's an Alliance operative, working for the central command, and with huge autonomy. (See Serenity - explicit in one of the trailers, even.)
The implications are that Book may have been similar level, but it's clear that Early also has access to the data records of the Alliance and KNOWS Book's past.
So the implications are, "Mal, do you realize you have an Alliance agent in your crew?" in an attempt to break the cohesion of the crew.
In Serenity, Book tells Mal that he wasn't always a shepherd and also that he doesn't have to tell him about his past, leaving it mysterious but implying something interesting.