As typical for a ZAZ! production, if you're not laughing every 30 seconds, it's because you're watching Top Secret! on cable and there's a commercial break.
But if you want examples of Funny Moments:
Omar Sharif doing everything in his power to play the spy tropes serious, which only makes the movie funnier.
How Sharif survives the car compacter. At least the windshield wipers still work...
Nick's torture at the hands of the Germans. He passes out and imagines himself back in high school, the day of the big exam. When he wakes up he sees he's still being tortured.
Nick (relieved): Oh, Thank God.
The entire scene of entering the Swedish used book store (with Peter Cushing!). Filmed backward, but executed flawlessly to appear going forward (well, except for them going upward a sliding pole and the dog).
When Nick and Hilary make love, they roll passionately on the floor and the camera tries to discreetly turn to a nearby fireplace. But the couple rolls into view again, forcing the camera to discreetly turn again to yet another fireplace.
And when they parachute with the French Resistance to rescue Hilary's father, they embrace yet again in mid-air... with yet another fireplace floating on its own parachute.
Du Quois: This is Chevalier, Montage, Detente, Avant Garde, and Deja Vu. Deja Vu: Haven't we met before? Nick: I don't think so. (Deja Vu nods, but then glares at Nick like he remembered something) Du Quois: Over there, Croissant, Souffle, Escargot, and Chocolate Mousse.
"How ironic! Another day and I would have completed my tunnel!"
And you have to see the tunnel...
But why would he want to escape to Joisey (according to the sign in the tunnel)...
"No, that doesn't sound like Mel Torme."
Nick: "Listen to me Hillary. I'm not the first guy who fell in love with a woman that he met at a restaurant who turned out to be the daughter of a kidnapped scientist only to lose her to her childhood lover who she last saw on a deserted island who then turned out fifteen years later to be the leader of the French underground." Hillary: "I know. It all sounds like some bad movie." (Beat, as the two turn slowlytoward the camera.)
For added hilarity, watch the movie with someone who has never seen it before. Shout "IT IS!" After Hilary's line right before the beat. See the look on your friend's face. Priceless.
When La Résistance is attacked in their shed, there are closeups of feet running in one direction, and then the other direction, and then breaking into a synchronized dance routine.
Nick and Hilary's ridiculous dance routine. A ZAZ trademark they would use in The Naked Gun.
The ad-lib for the song "Spend This Night With Me".
"Oh, honey dumpling, I promise I'll even be nice to your momma".
Nick and Hillary are riding in a hay wagon on their way to see The Torch; we hear a German drinking song being sung, and assume it's the driver. But the close-up shows us that it's the horse pulling the wagon who's doing the singing. As Nick and Hillary get down from the wagon, the horse lets loose with a hacking cough.