OK my favorite pokemon is Muk(shocker! :o!!). But the main reasons I like Muk isn't because of its uniqueness or because of its special qualities but more of how I learned to love Muk as a pokemon. In the anime there was never a point in the anime where I didn't like how Muk was portrayed(sans under the ownership of a villainous gang...as most poison types). Anyway I always adored how ash's muk was always friendly and affectionate towards everyone it met despite being a pokemon that is usually avoided. I also loved how Muk is also mostly just misunderstood; as portrayed in the episode where 3 Muk enter a pond and mucked up the water unintentionally driving out the psyduck. Its until they are sent blasting off into another swamp and finding three Muks(females) that its realized they just wanted a home too , just like all pokemon need, although they happened to ruin the pond.
What really sealed the deal is when I visited Dr. Footprint in my platinum and showed him my Muk and he told me what my Muk thought about me: "There are no Pokémon that dislike humans... Only humans that dislike Pokémon... We Muk are especially shunned... But [My name] always treats me as a friend and partner...". That is what made me want to make Muk my favorite pokemon. Not too many people would want to have a Muk, so I would be the one to take one in with open arms and be the best partner a Muk could have(Garbodor reference).
Now, being Muk and all his awesome glory he also does have several unique things about him that few other pokemon have. In the anime and games Muk has shown to be able to alter his body shape and size as well as certain gelatinous properties which I think is really cool and only I think the other pokemon with similar qualities is swalot(another one of my faves). With this Muk like many other poison types can control their toxicity and stentch(as displayed in the anime) as to not unintentionally harm anyone. Similar to how someone can hold a croagunk's hand without getting poisoned or someone can ride a rapidash without getting burned. I believe that truly displays how Muk is truly more of a peaceful pokemon as opposed to how some people view it as a pest and unlovable(yet a wild one would still respond how most any pokemon would if you introoded on its home or territory).
Muk is also very competent in battle as being both defensive and offensive. While also being able to accommodate more of a supporting role and live up to the reputation of how frustrating poison types are to fight. With moves such as minimize, memento, disable, and the obvious poison ailment Muk has several options to strike dread into the hearts of his adversaries. Not to mention also being able to use various elemental moves.
So that's my wall of text of why I like Muk.
EDIT: Since I basically slammed my entire idea of my event submission in that one post I'll draw something instead