These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Many people have noted that there's something oddly terrifying about the theme tune. Bill Bailey once suggested there was a 'secret hidden Satanic verse' about Zebedee having his legs cut off.
Periphery Demographic: Back in the days before kids' animation shows were expected to catch an additional geek audience, Thompson's whimsical humor surprised people by appealing to adults so much. It probably helped that The Magic Roundabout was shown on UK TV immediately before the news - the first adult program of the evening - so a lot of adults just home from work first caught it by accident when they turned the set on a few minutes early, or had an excuse for turning it on at that time.
What Do You Mean, It Wasn't Made on Drugs?: The general aesthetic and atmosphere are reminiscent of the more innocent and whimsical end of psychedelia, and there are particular allegations of drug references involving Dylan the hippie rabbit.