I don't think anything the show did was as goofy as the Rainbow Batman, or the team-up story where Superman brainwashed Batman into developing a second personality as a different superhero because he thought it would be a fun challenge for Batman to solve the mystery of who the new superhero was. And that's before you even get into Bat-Mite and the Batman of Zur-En-Arrh. '60s DC Comics were absolutely insane.
Of course, a large part of the reason for that was that the Comics Code had pretty much wiped out the supervillains or reduced them to minor nuisances, so the writers of the comics couldn't really tell stories about crimefighting and thus had to resort to creating weird mysteries or having the characters behave strangely for reasons that would be explained at the end of the issue. One of the changes Julius Schwartz made when he became Batman's editor was to reintroduce Batman's rogues' gallery, and he did this specifically because he thought it would help the TV show that was being developed at the time, that it would be more successful if Batman and Robin could fight colorful celebrity supervillains rather than the generic thugs that George Reeves had to settle for as Superman (and of course he was absolutely right). So as a result, the show (and presumably the comic series from that point onward) was able to tell more straightforward stories about battling crime, while still retaining some of the wilder elements of earlier comics. Since they could have actual villains to drive the stories, they didn't have to rely on "Why is Batman acting so strangely this week?" stories like the comics did for so long.
Of course, a large part of the reason for that was that the Comics Code had pretty much wiped out the supervillains or reduced them to minor nuisances, so the writers of the comics couldn't really tell stories about crimefighting and thus had to resort to creating weird mysteries or having the characters behave strangely for reasons that would be explained at the end of the issue. One of the changes Julius Schwartz made when he became Batman's editor was to reintroduce Batman's rogues' gallery, and he did this specifically because he thought it would help the TV show that was being developed at the time, that it would be more successful if Batman and Robin could fight colorful celebrity supervillains rather than the generic thugs that George Reeves had to settle for as Superman (and of course he was absolutely right). So as a result, the show (and presumably the comic series from that point onward) was able to tell more straightforward stories about battling crime, while still retaining some of the wilder elements of earlier comics. Since they could have actual villains to drive the stories, they didn't have to rely on "Why is Batman acting so strangely this week?" stories like the comics did for so long.