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.
It's also quite a hit in Japan. International audiences in general tend to like the show.
Growing the Beard: A Grand Day Out isn't necessarily bad, but it's far more Surrealthan the later episodes, Wallace's only invention is the rocket, and the "bad guy" is merely misunderstood and takes the form of a... robot oven. With The Wrong Trousers, Wallace became far more of a tinkerer, Gromit became the archetypal Silent Snarker and the series received a massive Animation Bump.
Which comes full circle in Project Zoo, which involves those same gameplay mechanics at one point.
Moral Event Horizon: During his malfunctioning, Preston attempts to turn Wendolene and the sheep into DOG MEAT!!! Surely that qualifies.
Lord Victor Quartermaine is willing to kill the Were-Rabbit (even though he knows it's really Wallace) just so he can marry Tottington for her fortune.
Nightmare Fuel: Piella is a surprisingly terrifying villain, due in part to being a serial killer.
Also the part near the beginning of A Close Shave when Wallace panics about Shaun going through the machine can be pretty alarming & disturbing to kids, especially because of the tense background music. Leads to Mood Whiplash when all it does is shave him bald.
The revelation that Preston is a robot, especially when he rips himself out of the machine.
Both transformation scenes from Curse of the Were-Rabbit.
The 525 Crackervac from the Cracking Contraptions short of the same name is kinda freaky in appearance with its red eyes and snapping metal teeth.
Tear Jerker: When Gromit runs away from home in Wrong Trousers and when Gromit cries over Wallace's apparently dead body in 'Were-Rabbit.
Another example is in "A Close Shave." In the last newspaper with the headline of Gromit going to jail for life that Wallace and Shaun are reading, both have tears in their eyes, as do several other sheep reading with Wallace and Shaun, as Wallace says, "Oh, Gromit," before he and the sheep look at a portrait of the two together.
Also in The Curse of the Were-Rabbit, there's Wallace's reaction to learning that he's the were-rabbit everyone's been hunting. He starts desperately trying to fix a device that might reverse the process, only to find that his brain is pretty much "rabbit mush". He ends up breaking down, sobbing "Oh Gromit, I don't want to be a giant rabbit!"
Again from The Curse of the Were-Rabbit: Victor locks Gromit in a cage while he goes after the Were-Rabbit (Wallace). Gromit desperately tries to get out for a few minutes. Then he slumps, and, even though there's no sound and we can't see his face, it's clear that he's crying.
The Woobie: Gromit, particularly in Wrong Trousers. Fluffles also qualifies up until the end of Loaf and Death.
Fluffles is probably the most Woobie character in the franchise. Piella hit her and you could literally hear her yelping in pain! It is also vaguely implied that she has suffered this abuse for quite a while
Wallace at the end of A Close Shave. After everything that they had gone through up to that point to earn their happy ending, Wallace finds out that Wendolene is allergic to cheese and can't stand it at all.