is there much vulgarity?

I can't say for sure that it has no rude words or suggestive situations, but I don't think it's unsafe for work or unsuitable for children.
The humour is based on random weirdness, and the safety hazards are done in a very "ACME safe landing on your head" kind of way.
Example: Assistant pours acid on scientist's hand, announcer says "That could have hurt" - during "Ghosts" in series 1.

British humour at its best, in my opinion fine for the whole family.
Proof you don't need to be crude or gross to be funny.
forever a

My favorite episode "Casserole"(not sure if that's the exact title, but that was the subject) has interviews with people about the casserole craze and one person says
something that gets beeped out. I actually doubt that there was any profanity, but it was hilarious as the reaction of the interviewer was a smiling nod and then a clever glance to the camera. That's the best way I can describe it, but if season 2 ever gets released, check it out. It's BRILLIANT!