Jingle bells, Batman smells ... ?

Not that I'm aware of, but there are a range of regional variations in both the UK and USA.

In the US, THAT LITTLE DITTY IS MOST USED BY bART sIMPSON

Thanks.

More specifically, I'm wondering if the insertion of these lyrics in an original song (with no other mention of Batman and Robin in the song and nothing offensive associated with them) could create any potential problems in relation to the current owners of Batman and Robin (Warner Bros). For example, suppose the hypothetical song I just described got played on radio and the writer received payment for the radio plays. Could this be credible grounds for the owners to claim a share of the proceeds -- if not by dint of copyright, then perhaps by trademark law or something similar?

Yes, I've come across that. Apparently there's documentary evidence of those lyrics existing in the 1960s, but no claims of ownership of the copyright (quite possibly put together by some school kids having a laugh).

This site does not offer legal advice, this is just guess work..

If anyone has copyright it's the writer of Jingle Bells, and I imagine that has expired.

I don't think the brief mention of a character affects copyright either. David Bowie didn't have to pay royalties to T Rex after All the Young Dudes.

Catatonia didn't pay the creators of the Xfiles to use Mulder and Scully.

If your hypothetical case had any teeth I'm sure the Simpsons would have been sued already.

I know, a real anaemic version, no mention of Mr Blobby at all.

It has become a song like "Holy motr phucking sh" or that British song about feminist....etc. It's origin is a commercial spot on FOX KIDS, and is just a fun car song when somebody farts in par or something like that. Funny song in school. At the moment no it is not. Besides it is free marketing.