According to Jerry Mathers' biography, the reason he won the part of "Beaver" is because he wore his Cub Scout uniform to his audition, and actually left the audition early to go to his den meeting!

Unfortunately, Mathers never says another word about Scouting for the rest of the book. And in the show, apparently, the only mention of Scouting is the "Lonesome Beaver" episode in which Wally goes camping with his Boy Scout Troop, leaving Beaver behind.

Does anyone know if Mathers finished Cub Scouts? Did he go on to join a Boy Scout troop? And was there any other mention of Scouting in the series beyond the "Lonesome Beaver" episode?

There was one ep (I don't remember which one) in which the closing epilog scene was nothing more than a recruiting ad for the Explorer Scouts. The scene had nothing to do with the rest of the episode.