In classic British style, much of the verbal humour especially is likely to sail right over the kiddies' heads. The most audacious example is probably in the Christmas Special, wherein a sadistic, whip-wielding prison guard tells Baynton, "I think I can speak for all the lads when I say, 'You're our favourite prisoner'." Yes, they actually went there.
There's a song set in a monastery featuring errant monks partying with a "funky nun" while the bishop isn't looking. Her closing thoughts? "Ah, men!" A cleverly PG presentation of what were basically orgies behind monastery walls between nuns and monks.
The Black Spot: A fearful pirate points out a black spot on the face of a nearby waitress. His friend assures him it's only Warty Wendy who was "born like that" before adding under his breath "She's got another one."
Bob Hale gets off a lulu in the Pharaoh Report: "Tutankhamen's daddy became a mummy, which is a very complex operation."
There's also the wink and lip-bite George II gives the camera (and repeats in the the Prom special) while singing the line "I was the bad one..." Not to mention George I singing about how ladies "would do anything for me, or I'd have their husbands killed..." with a big eyebrow raise on "anything".
Also from the Prom special, the inset sketch involving a royal lineup to use the public loo features this little experiment in just how much you can get away with by claiming historical accuracy:
Charles II: Henry VIII's in there with his personal bottom-wiper. Calls him the Groom of the Stool. Very popular job in his day, apparently... [aside, to George III] Not my kind of party, but to each his own...
Apparently, the Cash My Sin number (a riff on the medieval Church requirement that you pay to keep out of purgatory) is 0800-I've Been Naughty. Dang.