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During the finale, Neo kicks the Agent. He proceeds to leave his leg stiff, foot above waist level as he moves it from facing forward to facing his side, then slowly lowers it. Surely intended to be dramatic, but it came across as silly.
The way he nonchalantly says "no" sounds less like a man commanding bullets to stop and more like telling a cashier whether he wants fries with his burger.
To be fair, once Neo gets his God powers, stopping the bullets is probably as simple as telling a cashier whether he wants fries with his burger. If he had to do an epic "NOOOO" then it would have falling into Narm territory. His quiet "no" was a simple denial of the bullets' threat.
The bit where he fights the Agent off with one arm whilst looking slightly bored.
"...There is no spoon." It's supposed to be profound and philosophical, but Keanu Reeves' delivery makes it hilarious.
In Neo's climatic battle with Smith, his mighty slow-motion punch to the face is suddenly rendered hilarious by Hugo Weaving's comically distorted face on impact.
Whilst hanging on for dear life above a twenty-foot drop, the building which Neo is hanging onto shakes slightly, drawing attention to the fact that the scenery was made of styrofoam. It was funnier than the scene was originally intended to be.
Agent Smith's monotone interrogation was actually hilarious due to the delivery. Until the bugs show up.
Neo and Trinity walk into a building and shed their cloaks, each carrying eight guns.
Neo referring to a major theme of the trilogy during the final battle: "Because I... choose to."
Pointed out by The Nostalgia Critic, the liberal use of the words "choice" and "purpose" in the trilogy makes lines where one of the words is shoehorned in, like "let's move with purpose", unintentionally funny.