Zaphod is put in the room where he will be killed by psychological overwhelmingness by being shown his significance in comparison to the entire rest of everything in the universe... and lives. Albeit, because he's actually in a virtual reality specifically created for him to explore, where he is the most important thing in the universe.
Our loser hero Arthur Dent escapes certain death by learning to fly.
Upon arriving at a party held in a house flying far above the surface of a planet, Arthur discovers that Trillian's being given a hard time by Thor (yes, the Norse god of thunder. It's... it's complicated.) He gets protective and Thor takes offense. With one line, Arthur becomes the ultimate form of Unfazed Everyman, tricking Thor into removing himself from the area:
"Would you like to step outside?"
Another Arthur example. Summing it up wouldn't do it justice, but realize that the robot mentioned in the following paragraph has xenophobia, homicide, and world-ending destruction programmed into its mind and has proven throughout the novel that it is more than equipped to act on said programming...
He hurtled towards the astounded robot from behind. It still had its multifunctional battleclub raised...
With a sudden mad outburst of strength, he [Arthur] wrestled the battleclub from the startled robot, executing a dazzling banking turn in the air, hurtled back in a furious power drive and with one crazy swing knocked the robot's head from the robot's shoulders.
So Long, and Thanks for All the Fish
The prologue, a Call Back to the prologue of the first book:
And then, one Thursday, nearly two thousand years after one man had been nailed to a tree for saying how great it would be to be nice to people for a change, one girl sitting on her own in a small cafe in Rickmansworth suddenly realized what it was that had been going wrong all this time, and she finally knew how the world could be made a good and happy place. This time it was right, it would work, and no one would have to get nailed to anything.
Sadly, however, before she could get to a phone to tell anyone about it, a terribly stupid catastrophe occurred, and the idea was lost forever.
This is her story.
Ford bluffing his way past a crapload of armed security officers to smuggle himself, Arthur and Fenchurch onto a very public spacecraft.
Ford breaking out of the Guide building with everyone trying to catch him and still finding time to rip off the entire place. (It's under new management.)
Coupled with the Running Gag of him finding new and inventive ways to bankrupt the company using a stolen credit card. In one instance, he dials the Speaking Clock from a distant galaxy, collect, and then forwards the charges to the Guide.
Specific to the film
Slartibartfast showing Arthur the "factory floor" and Earth 2.0. Arthur is unsurprisingly floored.
To clarify, Marvin wipes out an entire Vogon army with one shot from the P.O.V Gun, making them all as horribly depressed as he is. Note this was after he was shot in the back of the head by a laser gun.
Vogon Troops: (entire army collapses) I'm soooo depressed.
Zaphod avoids being a complete Karma Houdini for accidentally having the Earth blown up thanks to Trillian sicking the POV Gun on him. True he steals it away from her a moment later but, it seemed to have an impact.
Zaphod: Why so edgy, baby doll? Relax.
Trillian: Why so edgy?! You wanna know why I'm edgy?! (fires the gun at Zaphod)