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A deleted scene has a rancor accidentally sitting on Ventress. As Anakin and Ahsoka escape, the Rancor looks confusedly to right, then to left, then jumping up and grabbing on to the ceiling with a painful yelp, as we hear Ventress' lightsaber activate.
In another deleted scene Ahsoka tries to empty the cargo hold of the Twilight, so they can gain some speed, by opening the hatch manually. After she almost fell out, she goes back to the cockpit, cockily remarking that it wasn't easy but she found a way, only for Anakin to point out, the hatch controller was right under her nose, on the console board.
In "Ambush," during Yoda's curb-stomping of the whole droid army, he goes inside a tank. All the droids try to run away with this dialogue:
"Run for it!" *two droids get pulled back into the tank*
"But I just got promoted!"
In "Rookies", Rex's plan to take back the Rishi outpost from a squad of Commando Droids? Just walking up to the door dressed in his own armor and saying "Roger, roger." What does he do when the droids ask him to take off his helmet? Hold the severed head of a Commando right in front of the camera. And Cody's reaction to this plan (even more hilarious considering that Commandos' eyes glow when they're active).
In "Dooku Captured", the pirates invite Obi-Wan and Anakin to join them for a party. They have the drinks drugged, but while toasting the Jedi wordlessly and seamlessly use the Force to switch their drinks with their neighbors'. The two enjoy themselves while two of the pirates are collapsed over the table.
Earlier in the episode:
Dooku: Is it civilized?
Hondo: That depends upon your definition of 'civilized'.
This exchange from a bit later:
Dooku: (about Hondo's gang) They are devious and deceitful, and most importantly... [beat]...stupid.
Obi-Wan: It's a wonder you don't get along with them. You have so much in common.
In the next episode, Obi-Wan, Anakin and Dooku are chained together by the same pirates. Hilarity Ensues. Probably the best, after too many old man cracks aimed against Dooku:
I would kill you both if I didn't have to drag your bodies.
Jar Jar taking out the pirate tanks by himself is one half hilarious and one half awesome.
In "Jedi Crash", Anakin waking up to the sight of a bunch of Lurmen staring down at him:
Anakin: Um, Snips??
From the next episode "Defenders of Peace" Lok Durd seeing an armed defoliator shell rolling towards him. The fact that it's George Takei only makes it funnier.
Help! I'll be defoliated!
At the end of "Mystery of a Thousand Moons", Captain Rex's deadpan reaction - while lying on a stretcher and recovering from a lethal virus - to the idea of training Jar Jar Binks to use a blaster.
Captain Rex: I am not training him.
Todo 360 realising that he doesn't have any memories of memory crashes from "Holocron Heist".
In "Cargo of Doom", Anakin goes Papa Wolf on three droids after Ahsoka is captured by Cad Bane.
Droid 3: (to Cad Bane) Sir, a-a Jedi is coming! He looks very unhappy. *screams in terror as Anakin cuts him apart*
Obi-Wan's somewhat morbidinterest in the Geonosian brain worms in "Legacy of Terror", even as Queen Karina has one ready to be placed up Luminara's nose.
Obi-Wan Kenobi: Come now, the ear or the nose? Which will it enter?
Anakin Skywalker: (in slight disgust) I'd say the nose.
Then when Anakin kills the worm while Obi-Wan was holding onto it for further study.
Obi-Wan Kenobi: I was going to study that!
Anakin Skywalker: Study the bottom of my boot!
Then there's the episode where Grievous and a group of Battle Droids are stranded on a planet with Rex and some clones. At one point Grievous and the droids find a herd of horse-like animals. Naturally they use them for transport... except Grievous dosen't let any of the Battle Droids ride the animals. He then expresses confusion as to why the droids have to keep stopping to rest.
Random Battle Droid: You wouldn't let us ride on one those creatures with us, sir. If you would allow us, maybe we wou- OH MY GOD!
Grievous: RRAAARRRHHH!!! (slices the droid's head off with a lightsaber) Any more complaints?!
In the same episode, Rex being licked by some of Cut's farm animals can earn a chuckle or two
Obi-Wan's reaction to Anakin calling Duchess Satine his girlfriend.
Obi-Wan: Don't worry, just catch them when they fall.
Rex: (speaking from experience) A lot of the General's plans involve falling.
Indeed Rex does speak from experience. Back in Landing at Point Rain, after taking out the wall of gun emplacements, Ahsoka flings him off the wall with the Force as the two jump after them. Rex is screaming all the way down until Anakin and Ahsoka catch him at the bottom.
Rex: "Next time, just tell me to jump."
Anakin: "Now where's the fun in that?"
Also in "The Zillo Beast Strikes Back" and a bit of Black Comedy, this exchange between two clone troopers just before the Zillo Beast breaks out of the research facility and they get crushed by the doors.
Obi-Wan: A republic military presence is the only sure defense against the Separatists Satine: Even extremists can be reasoned with! Obi-Wan: If one can be heard over the clanking of theirbattle droids! Satine: The sarcasm of a soldier! Obi-Wan: The delusion of a dreamer!
What sells the moment is Anakin's Pass the Popcorn face during the above exchange.
The part in "Supply Lines" when Jar Jar was distracting the Trade Federation delegates with... art with table-ware. And when Lott Dod found out about the supply ships to Ryloth? He just looked at Jar Jar, and he waved back at him.
Making it funnier, Dod was the only one at the dining table not amused by Jar Jar's art and gives his own aide an angry face for appraising it before the aide frowns with disappointment.
The general premise of "Sphere of Influence" can be one in context. It's essentially George Lucas (or rather, a Pantoran George Lucas look-a-like) vs. Greedo, especially when George himself has been seen wearing a "Han Shot First" t-shirt. And guess what, Greedo doesn't get to shoot at all when confronted with Papanoida.
Vos breaking in Mama's hut.
Obi-Wan: Vos! Somebody lives here.
Quinlan Vos: Ugh! Smells like somebody died here.
Obi-Wan: (apologizing to Mama) Thousand pardons, Madame. He hasn't mastered the concept of knocking.
When the Son admits to attacking his father in Altar of Mortis. The flippant way he describes the situation and twiddles his fingers is very darkly humorous in an otherwise super serious arc. See it here.
In "Pursuit Of Peace," a pair of bounty hunters pursue Padme in a high-speed speeder chase through Coruscant. Eventually, the chase zooms past a pair of parked cops, one of whom drops the coffee he was drinking in a classic "surprised cop" scene... and then it hits when you realize that not only are the cops droids, but they don't even have mouths to drink with.
"Fine, we'll do it the Wookiee way."
Oh, Jinx has a couple gems. "That's great, but it might as well be Coruscant as far as I'm concerned. We have no ship."
Jinx attempts to use a Jedi Mind Trick on a Trandoshan; it fails. Chewbacca punches the Trandoshan in the head, Jinx tries the mind trick again and it succeeds.
A few minutes later, Jar Jar and Senator Tills getting out of the whirlpool, holding onto eachother, while slowly spinning around. Sadly, it's part of the episode's Downer Ending.
In "Shadow Warrior," the over-the-top look of utter horror on Jar Jar's face when he realizes that his meeting with the Separatist forces on Naboo will be with none other than General Grievous himself is hilarious. It isn't until General Tarples very collectedly pushes down one of his upraised arms that his expression changes.
"Prisoners" had Tamson damaging Padme's helmet and the water starts to fill, threatening to drown her. Then Jar Jar sealed the hole with his spit.
"Great, it's gonna be another one of those planets." 
"Friends and Enemies": Rako Hardeen, Cad Bane and Moralo Eval arrive in a settlement on Nal Hutta. They decide to switch out of their prison fatigues and switch to something less conspicuous. What's one of the first things Bane gets? Another Nice Hat to replace his old one.
Later in the same episode, Ahsoka recognizes him because of said hat.
Cade Bane (to Obi-Wan Kenobi, disguised as Rako Hardeen): What are you looking at? It's a nice hat.
When the warlord in "Bounty" expects his bride, he instead finds that Ventress has switched her with Boba Fett.
When Obi-Wan and Ventress are forced to team up against Savage and Maul, they find themselves outmatched and have to flee. Obi-Wan uses this opportunity to lampshade Ventress' tendencies to flee when outmatched:
Hondo: And leave you alone with the two crazies!? [Beat] ...Well, okay.
And when he gets called out for his insolence.
Hondo: Insolence?! [laughs] We are pirates! We don't even know what that means!
Really, anything Hondo says usually subverts normal cliche Hammy-ness. And it's glorious.
In "War on Two Fronts" Ahsoka and Lux reminisced of their adventure on Carlac, which made Steela suspicious, or curious at the least. When she asked them what happened there, Lux gave her a very misunderstandable reply. Ahsoka's expression when she realized what Lux's answer implied was quite funny:
Steela: What happened on Carlac?
Lux: Ahsoka's the reason I'm here and not with the Death Watch.
Anakin's smirking in the background whenever Ahsoka and Lux interact with each other is both hilarious and heartwarming.
Anakin telling Ahsoka to push her feelings aside and focus on the main objective is rather hilarious once you realize that he should take that advice himself.
Hondo delivers some weapons to the Onderon rebels. This draws the attention of a small group of commando droids, who attack. Hondo's response?
"Oh, my, look at the time."
The battle droids used for comic relief were a Base Breaker in the earlier episodes, but it was actually funny when one droid gets blinded and end up shooting one of its comrades.
Yet more Hondo in "Bound for Rescue", now drunk for your amusement.
[after being launched into the air] "I'M FLYING!"
"I may not be as young as I once was, but...I'm older!"
Ahsoka trying to threaten him:
Ahsoka: If you don't let me go, you're gonna wish you were born a protocol droid!
Hondo: Haha, sometimes I do anyway.
Ahsoka's reaction when she recognizes right away that the "Animal Instincts" are actually the younglings in disguise who came to rescue her is also priceless.
Hondo: Uh huh... and... what do you suppose that means? *gets thrown to the floor*
Hondo's explanation for helping Ahsoka and the younglings when he was willing to kill them the previous episode? "Today is a new day! And lucky for you today, I like children!"
When Dooku accuses Hondo of trying to auction him off to the highest bidder back when he was Hondo's prisoner, Hondo simply asks if Dooku can blame him, since a Sith Lord would fetch a great price.
It's especially funny because he says as if he meant to compliment Dooku for being such a valuable hostage. Dooku's reaction is priceless.
In A Necessary Bond, another good droid moment is when one calls Grievous to tell him they're under attack, and is so busy giving the message that both Zatt and Petro just run up and slice him to bits in the middle of it.
R2 in "A Sunny Day in the Void". He doesn't take sass from a wannabe officer. What seals the deal is how he takes the Separatist code module and waves it at Gascon, practically mocking him. In fact, much of the humor in that episode comes from R2 totally ignoring Gascon and WAC's fighting over leadership and constantly proving himself the most competent person in the squad - all while neither of the main characters notice.
WAC-47 asserting authority in the end of the episode. Ben Diskin must've had a blast recording it.
In Eminence, the surprised moan Embo gives off when Savage knocks him off his feet.
"So the only thing you can tell me is that I will find Jabba... at Jabba's palace?" It's the expression on Maul's face which really sells it.
Bo Katan's line after Maul and the Death Watch's plan to negotiate with the Hutts ends in a battle with the Hutts' bounty hunters.
Doubling as a Crowning Moment of Awesome, Embo using his own hat as a snowboard. This becomes funnier when you realize that this arc was originally part of Season 5 but was officially released after the 2014 Winter Olympics.
Then there was Mace and Jar Jar's interactions during The Disappeared two parter, with Mace playing the straight man to Jar Jar's wackiness.
a Frangawl cult member (During the first part) was about to attack, but Mace just looked at him and the guy ran away screaming.
Near the end of the second issue, as the Shadow Collective forces on Ord Mantell are about to be executed by General Grievous' droid army, Gar Saxon (a Mandalorian) gives the rest of his forces an It Has Been an Honor speech. Ziton Moj gives him a less than enthusiastic look. Thankfully, Maul forced Grievous to shut down the army before they could gun his men down.
In Issue 4, Darth Sidious's response to Mother Talzin restoring her body.