At the beginning of the first episode of his Skyrim Let's Play he sings a rendition of Harry Partridge's Skyrim song that is surprisingly well done.
In part 49. After leaving the Thalmor Embassy, he accidently left one of the jewels for a quest there. Getting back into the Embassy is nearly impossible without mods, so he gets over the wall by exploiting a glitch where he uses his horse to jump over the wall! Also doubles as a Crowning Moment of Funny.
At the end of part 83, Jesse and Esbern are fighting an annoying Thalmor Wizard who keep running away from them and nearly kills Jesse. Jesse has enough and finishes him by stabbing him right as Esbern throws a fireball, creating a cinematic explosion. Followed by Esbern giving a one-liner
Jesse: He did not just say "I'm getting too old for this". Old man. I. Love you.
In the last episode of Deus Ex: Human Revolution: The Missing Link, Jesse is given a choice of saving either hundreds of innocent prisoners or the only person able to testify against the atrocities of Belltower from the poison gas the Big Bad unleashed. His Kleptomaniac Hero tendencies pay off HUGE here, as he refuses both options and takes a third option. How? By deducing that the only possible third option would be in the only vent he never explored, due to being blocked by a crate he couldn't break. He then sacrifices the only shot of a Rocket Launcher he only received moments before to break the crate, enter the vent, discover the room where the gas is being distributed, and destroying it, savingeveryone.Holy shit!
The entire livestream for Final Fantasy VI he and several other members of The Game Station attended. Special points goes to Jirard, who not only played the majority of the game, but also stayed awake for 36 hours and that includes the time he was awake before the livestream. Right before going to attend a wedding as well.
Part 15 of his Dead Space 2 playthrough has him having to fly back towards Titan Station while avoiding massive pieces of flying debris. After smashing through the roof of a building and landing on his feet on the floor, Jesse busts out with AC/DC's "Shoot to Thrill". Made even better with the fact that the pose Isaac is in upon landing is very similar to Tony's landing pose.
TGS Podcast #50 which starts talking about educational games at 1:14:00 before going into Jessie's teaching methods at 1:21:19. For all the times he plays The Fool in his Left's Plays and videos, he details an insane degree of planning, dedication and intelligence when describing his methods.