Muppet Treasure Island has the epic musical number "Cabin Fever." It actually is mentioned again, but by a character who's insane enough that he could have just been imagining it (and his cellmates seem to think he did). Which brings us to the question: if one of the criteria is that it's never mentioned afterwards, can a BLAM be lampshaded?
Its BLAM status is pretty obviously intentional — it's a parody of Irrelevant Act Openers from stage musicals; it's an over-the-top musical sequence near the middle of the film with absolutely no plot relevance that no-one ever acknowledges again.
I'd like to get my hands on, Whoever wrote this script!
Plus, you know, cabin fever is just kind of like that.
Sesame Street once had a stop-action sequence about an orange that made no sense whatsoever. The orange bounces and shuffles its way along a kitchen counter as items attach to it, forming a face. When it is finished, the lights go down, a spotlight comes on, and it sings the "Habanera" from Carmen. This alone would almost qualify as a BLAM, but it gets better: the orange struggles with her tone on the "L'amor" bit, getting more and more atonal, and her face suddenlyexplodes. Moments later the pieces all fly back on, and she finishes the aria as if it never happened.
There was also a rather strange one in which an orange ball rolls along a roller coaster track, while illustrating how to count to three. Pretty standard so far, but for some reason the segment ends with the ball landing in a grinder, a hand turning the handle (three times of course), and the resultant powder being displayed to the audience as if to say "Ta-Da!" ... wait, what?
Is the alternate ending featuring the ball landing on a device that turns it into three cherries, topped onto three sundaes and have one of the cherries eaten by a girl any better?