Big Boss falling in love with the Cardboard Box, and claiming that he feels at peace when he is inside of it, as if it was his destiny for him and the box to meet. What clinches it is Sigint's disbelief at Big Boss using the box as a means of camouflage and saying that he doesn't wanna know what he means when he says that he feels safe inside the box promptly ending the conversation. Furthermore this gives a hilarious insight into why Snake (and even Liquid likes the box according to Super Smash Brothers Brawl) likes the Cardboard Box so much, it runs in the family.
SigInt: Uh... Snake? What are you doing?
Naked Snake: I'm in a box.
SigInt: A cardboard box? Why are you...
Naked Snake: I dunno. I was just looking at it, and suddenly I got this irresistible urge to get inside! No, not an urge - more than that. It was my destiny to be here; In the box!
Naked Snake: Yeah. And then when I put it on, I suddenly got this feeling of inner peace. I can't put it into words. I feel... safe. Like this is where I was meant to be. Like I'd found the key to true happiness.
Naked Snake: Does any of that make sense?
SigInt: Not even a little.
Naked Snake: You should come inside the box... Then you'll know what I mean.
SigInt: Man, I don't wanna know what you mean! Between you and Para-Medic, is everyone but me that is hooked up with the Major strange!?
Naked Snake: ...
SigInt: Yeah, well, anyway, I suppose even that dumbass box might make a decent disguise if you wear it inside a building.
In the end, Raiden decided to go forward to the original Metal Gear and kill Solid Snake there, complete with actual 8-bit graphics. However, he gets shot by Big Boss, claims that he should have killed him when he had the chance, then the screen fades to black. The last line involves Rosemary saying that there will probably be a MGS 5. And sure enough, Raiden does return as the main character in Metal Gear Rising: Revengeance, salvaging something out of the indignity the poor guy had to put up with.
The Secret Theater videos are all pretty funny! Sad they were left out on the HD re-release though. Most notable examples including:
Gotcha This Time: Snake slams butterfly-shaped C3 bomb too hard, causing timer to reset to 0 and detonate the other charges, destroying the hangar. His expression is priceless!
The Quick Version: Ocelot offering a duel when chasing the WIG with hovering craft. When he jumps, he instead hits the other door and tumbles outside into the water. As the screen blacks out, Snake gives a sigh of disappointment. In Japanese version, Snake say "You're pretty good".
Naked Snake: I ate a Russian glowcap and it charged up my batteries.
Naked Snake: What's wrong?
Para-Medic: I, uh... that's... that's great! Um, Snake, can you excuse me for a second?
Naked Snake: Sure.
(She leaves. Snake can still hear her.)
Para-Medic: Did you just hear that?
Sigint: Yeah. There's no way eating a bioluminescent mushroom would cause your batteries to recharge.
Para-Medic: What do you think it means?
Sigint: Beats me... maybe it's all in his mind.
Para-Medic: You mean like a placebo effect?
Sigint: Why not? You've seen how gullible he is.
Para-Medic: I guess there's no harm done. Should we let him keep believing it?
Sigint: Sounds good to me.
(She comes back)
Para-Medic: Okay, Snake, I'm back. Yes, the Russian glowcap is a glowing mushroom, so it'll recharge your batteries when you eat it.
Talking to the people in your codec list (call Eva last) with the crocodile hat on shows you that the word "normal" does not apply to anyone involved with the FOX unit.
The part when you rescue Sokolov. He follows Snake outside, imitating his MOVES, and somehow ending up with a Kamehame Hadoken gesture, at which point the camera pans over to Snake, staring at the scientist with a complete "What the frick are you doing?" look on his face.
ALL the Easter Eggs in the third game qualify. Take your pick: between the conversation between Para-Medic and SigInt about Snake and the glowing mushrooms, calling Eva after you call everyone else with the crocodile head thing on, wear the scientist suit in the jungle, etc.
If you get a Dragunov early enough, you can snipe The End as soon as you see him in his first cutscene and skip his entire boss battle.....though you do get smacked by a wheel from his wheelchair after he explodes.
During the conversation about vampire bats, Snake stops Para-Medic from talking about vampire movies. The examples he gives of B-movie titles include Attack of the Vampire Doughnuts and Dracula Versus the Space Hippos.