I think the end to "Other Space" definitely is an awesome moment for the Doc. He saves the earth (and probably the entire universe) from hostile invading extra-dimensional aliens, inflicts heavy damage on whatever place they came from, and survives being at the ground zero of the blast (which was considered impossible) using his inventions. Benton Quest may not look intmidating like Race, but if you mess with him and his family, he will mess you back with SCIENCE.
He shuts up an obnoxious reporter by snatching his mic from his hand and slamming it in his open mouth.
He gets one at the end of "Manhattan Maneater", when a small mob gathers under a subway to kill a tiger that's been wandering around. Before it can be shot, Race hits it with a tranquilizer, takes the gun off of the tough hunter, and bends the barrel with a huge hunk of metal lying around. When the slimy reporter waves a microphone in his face and angrily asks "Do you know what you did?", Race knocks the reporter over with said microphone and says "Yeah, I just shut you down".
He gets another one in "To Bardo And Back", when Jeremiah Surd turns into a bull (Race's greatest fear) and tries to either run him down or force him across a mystic river that equals instant death if crossed. After being chased for a minute, Race catches Surd by the horns, and picks him up and tosses him into the river. This forces Surd to change back, then Race curb-stomps his ass before shoving him to the other side of the river. Only the quick thinking of Lorenzo, The Dragon, saves Surd from dying.
In "Night of the Zinja", Race goes Papa Wolf on an android that had attacked Jessie.
Race: Protoypes are one thing, but that's MY DAUGHTER!
In the same episode as Race's encounter with the reporter, Hadji blasts that same reporter when he makes a blatantly racist remark about Hadji's turban.
In "Expedition to Khumbu," the Quest team is looking for Benton, who went missing after an avalanche in Nepal. Through a series of missteps, they end up hanging off a cliff, with Jonny and Hadji locked in a cage at the bottom, Jessie hanging in the middle, and Race up at the ledge, keeping them from falling with a pickaxe and the strength of one arm. Seeing as her companions can't actually move, Jessie unlatches her belt from the rope, climbs all the way down to Jonny and Hadji, all the way around to the bottom of the cage so she can pull the lever that gets it open (her impossible risk is promptly lampshaded by Hadji). When it does open, she manages to hang on to Jonny's leg to avoid falling to her death. Then she climbs up over Jonny and Hadji and up the length of the rope until she reaches the ledge (much to Race's relief), where she promptly helps her father pull the two boys up. Jonny says it best:
Jonny: Gotta hand it to her, Hadj—She's pretty cool.
In season 2, Surd uses Questworld to steal Jessie's mind, and torture the entire Quest family. In the end, she snaps out of it, temporarily gains full control of Questworld, and sends Surd somewhere in its depths, in a digital body just as infirm as his real one. "Nobody messes with my family" indeed.
In "Assault on Questworld" Jessie displays her willingness to use, and skill with, firearms.
In "Ezekiel Rage", believing that Rage had just killed Jonny with a nerve agent, she frees herself from his grip and triggers the fuel dump for his aircraft, then joins a very much alive Jonny in skydiving from the descending plane, just before it crashes into the canyon walls in a fiery wreck.
In "Eclipse," Jonny jumps from his hoverboard to hang off a flying succubus-vampire-like monster in an attempt to save Jessie. While hanging off the monster's tail with one hand, he manages to pull out a silver bullet from his pocket and touch the monster with it, hoping it would be enough to kill it. It doesn't work, and Hadji's the one who eventually brings down the monster, but wouldn't Harrison Ford be proud?
Jonny uses an experimental speed boosting device (worn sort of like an anklet) to run down first a motorcycle and then a plane as it's taking off.
In the very first episode, Jonny tricks a bunch of thugs into wrecking their own boat by going Guile Hero and pretending to drown.
He uses his Guile Hero tactics again to trick Lorenzo into dropping his gun, then revealing that he'd held Lorenzo at bay with a fire extinguisher. An enrage Lorenzo was about to charge Jonny when he heard his gun cock behind him and then we move into Jessie's Moments of Awesome.
In "Ezekiel Rage", he manages to hold his breath long enough to emerge from a cloud of toxic gas, slip aboard Rage's plane, and aid Jessie in her escape, already in progress.