A meta example: Depth Analysis, the studio that did all the motion capture for the game, released a blooper reel for the game. (Note: the link is a fan mirror uploaded to YouTube from the Depth Analysis website.)
Whenever you have Cole accuse a suspect of lying, only to have him back out, the manner in which he awkwardly backtracks to the main line of questioning.
The Vice department roadside mission "Camera Obscura", where Phelps and Earle are called to an elderly woman,
Old Woman: That lowlife! That filthy lowlife!
Phelps: What happened?
Old Woman: I was standing ready to get off and... I heard a click. His camera. That pervert took a picture of my...
Earle: *coughs uneasily*
Old Woman: ... of my ... *blows cheeks for emphasis*
Phelps: Which way did he go?
*cue cut to women shrieking across the street.*
Old Woman: There! That's him! Right there!
*A woman is seen who is chased around in circles by everyone's favourite next-door perv, Marlon Hopgood, bearing a standard 1940s 8-kilo camera. As he loses her he catches a glimpse of Phelps and Earle*
Hopgood: Aaaw, fuck!
*He runs to his convertible, nonchalantly tosses the monstrous camera on the back seat, and stumbles into the driver's seat without opening a door*.
And the whole mess is made even funnier when the fact is considered that Hopgood, a photographer and illegal porn producer as we learned in The Fallen Idol, is a police informer and originally deemed harmless by Earle (whom he knows personally). The same Earle who has to track him down with Phelps as he escapes.
Or the Vice side mission The Badger Game, where Phelps, Earle and a cop are called by a young black man, who sends them after some supposed criminals who apparently robbed him. As they distance themselves into the pointed direction, the "victim" just gives them a double-wide grin and skip-hops to the cop's car, which he promptly steals.
During the last Homicide case, Cole is about to head into a tar pit, to find a clue left on an island by the Black Dahlia killer. To do so, he changes into a pair of waders, which warrants much derision from Rusty. They really do look quite ridiculous on Cole.
Made even better when he glares at Rusty and puts on his fedora, because obviously if he's gonna go down in there, he'd damn well better have his hat on.
There's an idle car chatter moment during Phelp's time in Homicide that ends with Rusty shrugging off any idea of emotional intimacy between partners:
Rusty: If you want somebody's shoulder to lean on, crawl into bed with your wife.
Cole's Alas, Poor Yorick with a shrunken head replica and how he sheepishly clears his throat right after. Implied "Sorry, I couldn't help myself there".
And what he says right after he clears his throat:
Phelps: Is it real?
Made even better because this marks the only time Carruthers actually drops his stoic and professional demeanor enough to crack the hint of a smile.
The Drunk outside the bar in "The Driver's Seat." "Hey, I know you!" "No you don't."
What sells this moment is the drunk's enthusiasm in contrast to Cole's stern deadpan.
The same drunk appears at Cole's funeral, so either he did know him after all, or the exchange just made a strong impression on him...
Captain Donnelly making off with a case of Cognac from the fruit market at the end of one of the homicide cases.
When Donnelly pours himself and Rusty drink for the successful conclusion of a case, leaving Cole without one.
"You'll be calling Richard Nixon a crook next!"
At the start of the Traffic arc, Captain Leary introduces Cole to the other traffic detectives, telling him to take a bow. Cole says he'd prefer to sit, before Leary orders him to bow. Cole then stands and nervously bows. Hilariously accompanied by Sarcastic Clapping and Flat Joy.
Stefan Bekowsky's exaggeration of how Cole Phelps earned his Silver Star:
Bekowsky: You were up there all night, draped in the flag, knife between your teeth, gun at the ready...
Cole: You finished?
Bekowsky: The Emperor Hirohito himself leading the charge against you...
During The White Shoe Slaying, when Cole says to suspect Richard Bates "Do you want my partner to SAP YOU?" while Galloway menaces Bates with a small stubby police baton in a almost comical manner.
Earlier before this scene, Cole and Rusty enter the bar looking for Bates. Rusty's immediate response when they see him? 'LAPD! Don't make me chase you, shitbird!' His delivery is absolutely hilarious.
During that same mission, when you tell Lars about the murder of his wife, he is sitting on the sofa next to his daughters who look about 7 or 8, (Considering that in an earlier mission a high-school aged girl looks 10, they're probably a bit older) the 2 girls leave the room immediately afterwards, Lars follows them, and they basically scream "WHERE'S MOMMY?" at him.
Cole and Biggs setting up a whip round for the Steffans family during "The Gas Man", and putting fifty dollars in on Cunningham's behalf.
Bekowsky trying to impress June Ballard and getting shot down.
Bekowsky: What about me, June? I'm a big fan of Beast... June Ballard: No. You I don't like. Stay out of this.
During one of the murder cases when at the crime scene speaking to a suspect:
Cole: What were you doing with the corpse?
Jamison: You're gonna be upset if I tell you...
Cole: Try me, Ferdinand.
Jamison: Well... I was kissing her.
Rusty: [with no build up animation, no forewarning, immediately decks him]
And he keeps trying to do it, to the point where Cole has to restrain him. And then gets another shot in when Cole walks away.
Your partner's comments when you drive recklessly. Some gems include:
"Whaha; You're gonna kill us all!"
"Ugh, I knew I should've driven."
"Take it easy there, Phelps. I'd rather get there in one piece."
<clearly exasperated> "Watch out for the civilians!!"
"You're gonna kill them!"
"Slow down before someone gets hurt!"
"Can we try to get to the destination in one piece?"
"I think you're doing this on purpose."
"NOW look what you've done!"
"There goes our week's wages!"
"This is coming out of your wages, not mine!"
"You're paying for every last scratch!"
"Thank God we're not in my car..." (said by Earle if you're not driving his car.)
"You're enjoying this, aren't you!?"
"OPEN YOUR EYES!"
"Oh no...oh no, no, no! You did not just do that..." (Earle has a long pause after his last "no")
"Everyone! Run! There's a maniac on the loose!"
"Sorry! My partner ain't exactly the best driver in the world."** "I think you're actually aiming for these people!"
"That was a tax-paying citizen you just bounced off the FUCKING HOOD, Phelps!"
"Can we try not killing the people who pay our salary?"
"Are you trying to mow them down?/run them over?"
"God, this is like the war all over again!"
"God, this is a nightmare!"
"This ain't a tank, Cole!"
"Breathe, Phelps! Breathe dammit!"
"Are you blind?"
"You can see these people, right?"
If you choose a delivery truck, fire truck, ambulance: "Fine, but if the Skipper sees us driving around in this, we're dead." or "You've gotta be kidding me. We're driving this?!"
"I wouldn't feel safe in a tank with you driving!"
"You want me to keep tabs on the path of destruction you're creating?! It might come in handy at your trial!"
(after running over a pedestrian) Well, now you've either gotta stop, or put your fuckin' foot down!
"Try making it to the next intersection without killing anybody. Can you do that for me?"
(after running into another vehicle) "You got a siren, Phelps, or is this some form of stealth attack?"
Cole will occasionally talk back to them, increasing the hilarity:
"Maybe I'd drive better if you'd shut the hell up!"
"And at the next junction, you shut your trap!"
"If you want instructions on how to wipe your ass, you let me know."
"Left, and left, and left, then left again, and I'm right up your ass!"
Cole also has comments for when you successfully ditch your partner and continue the path of destruction:
"Are you stupid?"
"Just a scratch."
"You've got to be kidding me!"
"Son of a bitch!"
Or when you drive recklessly while tailing someone, your partner has a few things to say:
"Now would be a bad time to forget how to drive, Cole!"
"Only half the neighborhood saw that!"
Another one with Rusty while tracking a bus during a murder investigation:
Rusty: You shoulda gone around the other way. We would've caught up to it by now.
Cole: How could I have known that then?
Rusty: You gotta use your gut for these things. Your gut is clearly lacking.
Cole: And your gut lacks for nothing, Rusty. Though lately it's been requesting beer.
Rusty: Beer and convictions, Phelps. Beer and convictions.
Cole: Let's change the subject. Are you fasting for Yom Kippur, Mr. Kalou?
Kalou: Yeah, let's change the subject YOU GOY MOTHERFUCKER - how about baseball?!
Kelso sticking it to Roy Earle during his interrogation.
Kelso (to Phelps): You're trying to make a name for yourself with this shit-heel? Look at this chump, with his 200 dollar suit and his 2,000 dollar car!
After the massive explosion in Nicholson Electroplating Ray Pinker assures Biggs and Phelps of their safety in the most morbid way possible:
Pinker: It wasn't nuclear. If it was we'd all be dead from the radiation.
Biggs: That's reassuring. What's radiation?
In fact this case is filled with gallows humor, possibly as a coping mechanism for the horrors they're facing such as when a dead man falls out of a fridge Herschel ponders:
Biggs: Do you think I could fit in there? I couldn't fit in there.
Phelps: I'd like to think you would have had something more to say about getting shoved in a fridge, Herschel.
Later on in the case, Ray Pinker pulls a trick on Cole involving a miniature explosion. It's a funny moment by itself, but then Carruthers caps it of by saying, unamused, that Pinker got him with the same trick an hour earlier.
Made even funnier in a Funny Background Event, where Carruthers immediately hides behind a counter when he walks in. The gamer that notices this knows this won't end well.
The ridiculous expressions Frank Morgan makes while trying to cover his lies.
Touring the soup cannery with Roy in "Reefer Madness". Roy accuses Cole of checking out the secretaries, moans that seeing soup be made will spoil his appetite for it, compares the tour to a field trip and mocks Cole for being white-bread enough to find it interesting.
Also this exchange in the beginning of the case, upon Roy being told that he has to pay an informant $50 out of pocket and fill out an expense report later:
Roy: Fifty bucks? Do they think I'm made of money?
Cole: No, you just look like you're made of money.
Roy: Oh, very good. The kid's on form. I'd say on a scale of dull to scintillating, you're a solid tedious today, which you can be pleased with.
Then there is the scene if Cole decides to open the can with a Jack In the Box. Roy calls him out on being scared, despite himself be clearly scared by it.
Cole and Stefan in the DLC case, A Slip of the Tongue, after interrogating Jean Archer. The delivery from the three actors is what makes the scene.
Cole: Some career advice, Jean: get out of crime. Marry someone boring who has money and will find you captivating.
Jean: Is this guy for real?
Stefan: He takes a little getting used to. But yeah, he means what he says!
Or: Cole and Stefan are preparing to bust a car theft ring in a warehouse that's been confirmed to be loaded with bad guys.
Cole: *from behind the wall* Cole Phelps, LAPD. All of you are coming downtown with me.
Of course there is also the first talk with the car salesman. He seems a lot like a joker.
Richard Coombs: Well, some people would say that my cars are steal. *Beat* That's a joke, son.
Coombs: It's in my office walk this way. *walks in front like a drunken clown* That's a joke too, son.
Stefan: [to Phelps; beat] Phelps, do you mind if I shoot this guy? He's getting on my nerves.
Stefan: [after another "pun" from Coombs; whiningly] Let me shoot this guy... please?
He then goes on to compare the statement "Car Salesmen are assholes" to a Chicken-and-egg situation. Phelps proceeds to thoroughly discuss the guy's behavior.
In The Gas Man, when Cole accuses Clemens of being an arsonist he goes on a rant about how he burned down his home because his wife committed adultery and won it in the divorce settlement. Biggs shakes his hand.
Made even funnier for Angel fans as this is Connor and Holtz reuniting.
Roy complaing about how they have to tour the factory during Reefer Madness.
Roy Earle: "I hate seeing how things are made. It's like when I went to the slaughterhouse and couldn't eat steak for a week."
This moment in Manifest Destiny. Cole and Bekowsky are discussing the deaths of a four-piece band, when Roy Earle ruins the moment:
Stefan Bekowsky: Get this: They used to be in a four-piece but the trombone player and the drummed OD'd.
Cole Phelps: Don't tell me: Lamont and Tyree? We've met the rest of the band.
This brilliant piece of ambient pedestrian dialogue while tailing Candy Edwards in The Setup:
"Three blondes walk into a bar. You'd think one of them would have seen it."
The less than stellar controls for driving can lead into some gut busting moments for the player.* If you ditch your partner and manage to get far enough away, they'll need to hitch a ride from other cops to catch up with you.
Since cutscenes are triggered by your proximity to a certain area, it can be pretty funny to see your totally wrecked car inching it's way toward the crime scene, but parked perfectly in the cutscene.
Cole's exchange with Officer Hart at the railway, during the Studio Secretary Murder: