The phone conversation he has with (Doug imitating) Adam Sandler. The fact that Sandler is portrayed as being polite and mild-mannered makes it even funnier despite the Critic's hatred of him:
NC: ... In fact, I'm not gonna jump to any conclusions. I'm just gonna call Mr. Sandler right now, to figure out who did that voice. [does so]
NC: Mr Sandler?
NC: Nostalgia Critic, long-time fan of your genius. Uh, listen, I just have one question for you- who was that inspired old man who portrayed Whitey in Eight Crazy Nights?
Sandler: Uh... actually, I got a little secret for ya. It wasn't an old man at all.
NC: (faking) Whaaaaat?!
Sandler: No, actually this will totally blow your mind. Iiiit's me.
Sandler: It's meeee!
Sandler: Preeety amazing, huh?
NC: Mr. Sandler, I think I speak for all the world when I say that we, as a species, have seen actors become other people. But YOU, sir, YOU have taken it to a whole new level! You are like some sort of mutant chameleon that we cannot see just become other things! Other entities!
Sandler: Uh, oooh... Thank you so very much-
NC: Oh my god! And your CHOICE to have him in the majority of this film so that we can hear your BEEAUTIFUL instrument, I just have to say: THANK YOU! THANK YOU, on behalf of ALL the world for letting us be a part of this MAGIC!
Sandler: Oooh, I, uuhhhh... That's very kind of you to say-
NC: FUCK MEL BLANC!
Sandler: Uh... What?
NC: THE MAN OF A THOUSAND VOICES! THE VOICE OF ALL THE LOONEY TUNES?! FUCK HIM! HE IS SHIT COMPARED TO YOUR GENIUS!
Sandler: Uh... boy... whaaat? That's going a little far there...
NC: NONONO! IF I COULD FIND A WAY TO GET HIS BODY, AND PUT LITTLE UPSIDE-DOWN CROSSES ON IT, TO ASSURE THAT HE IS ROTTING IN HELL BECAUSE HE EVEN ATTEMPTED TO BE THE BEST WHEN HE KNEW THAT AT ONE POINT YOU WOULD BE BORN TO BRING US THIS WHITEY VOICE, IS AN INSULT AND I WOULD DO IT TO HIM TO MAKE SURE THAT HE SUFFERS FOR EVEN TRYING TO DO SOMETHING EVEN BETTER THAN YOU!
Sandler: Ooooh, uuuhhh... You're going a little overboard-
NC: MIIIIISTER SANDLER!
Sandler: Oooookay, I-
NC: IT WOULD BE AN HOOOONOR...
Sandler: You need to calm down-
NC: FOR ME TO DIG UP THE CORPSE OF MEL BLANC...
Sandler: Uuuuh, it's... I-
NC: SO THAT YOU COULD TAKE YOUR DICK...
NC: AND SHOVE IT UP HIS ASS...
Sandler: ...Oh god-
NC: BECAUSE THAT... IS HOW LITTLE OF A CANDLE HE HOLDS TO YOU...
Sandler: Uh, that's...
NC: HE HOLDS TO YOU!
NC: AND YOUR BRILLIANCE FOR WHITEY FROM EIGHT CRAZY NIGHTS!'''
Sandler: I, uuuhhhh... that's not really necessary-
NC: IT WOULD BE AN HONOR!
Sandler: Please stop saying that-
NC: AN HONOR, SIR!!!
) Okaaay... you're scaring me, and... I'm gonna go.
NC: THAAANK YOOOU, SAAANDLEEER!!!!!
Some more parts of the rant about Whitey's voice include:
Critic: "So, what's the only thing worse than listening to Whitey's door-nail-in-your-brain voice? How about if he sings with that door-nail-in-your-brain voice?" (Whitey sings a song. He hits a high 'E', and the Critic's ears explode) Aaand there went my eardrums! I should be sad, but I'm just happy I don't have to listen to Adam Sandler anymore. (sighs in relief) Ah, that's nice."
- The Critic saying that even Gollum would be pissed off at Whitey for ruining an emotional scene with his annoying voice.
Gollum: "Christ, buddy. You're killing Hanukkah!"
- After Davey's home is burnt down by another guy, Whitey offers him to stay at his place.
Whitey: What other options do you have?
Critic: You mean between "Freezing to death outside" and "listening to your voice"? (starts singing with glee) Let it snow! Let it snow! Let it snow!
Walken!Popeye: Olive Oyl... lets say you and I have sex and stuff.
Walken!Bluto: Olive Oyl, I'll also wanna bang you.
: Me? Okay, well I'm gonna do this weird thing where I'm naked and suddenly I'm not and BLOW!
- The Critic pointing out how annoying it is for Whitey to tell Davey's tragic backstory by comparing it to having Chris Tucker announce the death of your parents.
: OH MY GOD! YOUR PARENTS ARE DEAD! ONE MINUTE THEY'RE FINE, THEN BOOM! GONE! THEY BLOWED UP! GONE IN A FIREY INFERNO! KFP: KENTUCKY FRIED PARENTS! CRISPY! EXTRA FRIED! OH MY GOD, THEY'RE GONE! GONE FOREVER! LIKE ME AND RUSH HOUR 4
! EXCEPT THEY DIDN'T MAKE IT 'CAUSE JACKIE
'S LIKE A FAJILLION YEARS OLD NOW, BUT HE COULD STILL KICK MY ASS
! OH MY GOD! YOUR PARENTS ARE DEAD!
- "Ah, yes, and Eleanor's cry-snorting [throughout] makes the scene even more powerful. Jesus fuck, what do they do for an encore? Read The Diary of Anne Frank?" Cut to Anne Frank: The Diary of a Young Girl (As Read by Whitey)
Critic!Whitey: "....Despite everything, I believe people are good at heart."
Critic!Whitey: Quiet, Eleanor, you're ruining the weight of my incredibly dramatic voice! [gibberish]