Day of Disaster has the bridge technicians thinking Brains may be insane and have escaped from an asylum.
Even better when Lady Penelope rescues him from a psychiatrist and he catches her speaking into her makeup kit.
In "The Man from MI5", when they're in Monte Carlo, Lady Penelope gives Parker the night off. As he's leaving, Lady Penelope asks him what he's doing with the bag he's carrying. He starts to tell her that he's taking it in case he wins anything at the casino he's going to. Then the bag falls open and all his burglary tools fall out.
Later, Lady Penelope asks him how he did at the casino, and he admits, sadly, that he lost. She asks how much he lost, to which Parker replies that it was what he lost. After a bit more prodding and uncertain murmuring....
Penelope: Come on, you can tell me. Parker: Your yacht, m'lady.
"Vault of Death": Lady Penelope's driving. The funny part is seeing her guest and Parker are in the backseat, covering their eyes.
Several from "The Mighty Atom":
Parker and Kyrano fight over the drinks tray (notice that David Graham voices both characters at the same time).
Lady Penelope screams at the robotic mouse (off-screen).
The Hood crushes the robotic mouse after discovering photos of a terrified Lady Penelope.
Before that, after being told he and Tin-Tin aren't allowed to leave the base (despite Scott and Virgil being allowed without a second thought), Alan angrily declares he's going to bed. In a rather Seinfeld-esque moment:
Tin-Tin But won't you have some coffee, Alan?
Alan No thanks! It keeps me awake!
The ending of the episode "Cry Wolf", Tony and Bob let Scott drive in the cart they use as Thunderbirds 2, only for him to turn out to be too heavy for the cart and ends up crashing through the barn and into some rubbish bins, it's topped by what Scott says after his bumpy ride:
Several from "The Cham-Cham", both involving Parker:
Parker decks a sniper before he can shoot Penelope and Tin-Tin, but both end up rolling down the hill in a large Human Snowball.
After catching some hooks from Thunderbird 2 with an umbrella, Parker is launched from the cable car by the sudden stop. He is unharmed, though, since he floats to the ground with the umbrella Mary Poppins-style.
One commercial from 1993 had the traditional countdown— only for Thunderbird 1 to stay on its' launchpad, much to the bafflement of the narrator, who repeats "Thunderbirds are go!" again. Still no response. Turns out Scott's on break, eating a KitKat. At the end of the ad, the narrator frustratedly shouts "THUNDERBIRDS, GO!"
"The Stately Homes Robberies":
After Lady Penelope crashes the crooks' helijet, one of the crooks can be seen still trying to operate the controls even though the jet has been completely blown up.
When Lady Penelope is confronting the crooks, one of them can be seen waving his arms around like a child having a tantrum.
When Penelope and Parker are returning the jewels, Parker has a brief fantasy where he imagines himself as a king wearing the crown jewels. Penelope has to snap him out of it.
The 2004 movie
As a Mythology Gag to the series' use of human hands in close-ups, they did the inverse during the Thunderbird 1 launch- a puppet hand suddenly replaces Fermat's!.
When Parker is flying FAB-1 to Tracy Island, Lady Penelope is casually reading items from a newspaper, to which Parker replies in his usual stoic form. She then casually adds "Oh, and England won the football last night.", causing Parker to cheer wildly — and briefly lose control of FAB-1, tossing Alan and Fermat around before he regains control.
The Hood's Large Ham antics (along with his goons) can be pretty funny at times. Like when he has Brains activate the command and control center, he's taken off-guard by the room's rotating, and Ben Kingsley's facial expressions just sell it. He's probably thinking "Whoa, didn't expect this. Gotta keep my self from falling over."
When he tries to make Brains do it just before hand, his response? "Fu- Fa- Fu- NO WAY!" The Hood's expression indicates he didn't think Brains was gonna swear at him.
And when Jeff asks him who he is. He replies almost casually "Oh you can, call me The Hood.", while he's looking at the floor. What was he looking at? The stuff that made the room rotate?