I think THE WEB PLANET must rank-- absolutely must-- as the single most bizarre alien planet The Doctor ever visited in the entire history of the series! During the 1st episode, The Doctor is in unusually high spirits, delighted by every new phenomena and experience he encounters, and keeps laughing & muttering to himself in a manner that reminded me very much of Yoda from THE EMPIRE STRIKES BACK! It's obvious the TARDIS control room has been rebuilt between seasons. Apart from a few "roundels" near the doors, it looks almost nothing like it did during the 1st season. All the intricate computer banks are gone, replaced by mostly blank walls, and a section stuffed with unusual gadgets, including a movable "star map" which over the course of the story seems to double as a long-distance communications system.
Part 1 ends on a multiple cliffhanger, as Barbara, entranced, is walking straight for a pool of acid, Ian has been grabbed by a bizarre "web", Vicki, knocked about inside the TARDIS, begins hitting switches at random, and The Doctor is horrified to find his ship has-- disappeared! Ian & The Doctor soon find, in a bit somewhat reminiscent of the film THE TIME MACHINE, that someone has dragged the TARDIS away, and they follow the tracks on the ground. Before long, they find themselves in one of the WEIRDEST-looking sets ever (the production designer really went wild on this one!). Barbara, meanwhile, encounters The Menoptera, a race of butterfly-like people. The design, the performance (both speaking and movements), everything about them is just so "alien". Depending on your point of view, this story can either be looked at as the realization of a truly alien landscape on a microscopic budget, or as a children's pantomime-- maybe both. I was reminded quite a lot of watching the PETER PAN stage play. It's the sort of thing that may be difficult for anyone over a certain age to deal with, but I think it just takes deliberate effort on one's part to "get into" it. One thing I would highly recommend, DO NOT watch this in one sitting. It really works best in smaller segments-- like, one episode a day.
Late in the story there was much emphasis on The Doctor's ring, which is supposed to have some unusual properties (or powers). Was this the first time it appeared? I do recall reading about how it slipped off Patrick Troughton's finger when he regenerated. I don't suppose it was seen after that...