The opening narration where Shen is absolutely ecstatic about killing all the pandas is pretty creepy. The reaction of his parents when Shen bursts into the room with a look of sheer joy and excitement on his face is likely the same as the audience.
Shen himself is an incredibly frightening and intimidating foe. Let that sink in for a second: DreamWorks found a way to make a peacock, one of the goofiest and gaudiest-looking of all animalsnote Though not so goofy when you learn that pheasants are known to attack people in captivity, and that peafowl are often used to kill snakes, into a frightening, intimidating character. Who knows martial arts.
Tigress's glowing eyes during the boat scene is pretty creepy in itself. Note that this is a trait she shares with Tai Lung.