Other mistake: When walking through the Captain America display at the Smithsonian, Brody and Sam stand in front of a Captain America mannequin next to his shield. The mannequin is wearing boots of noticeably different heights.
The Falcon and the Winter Soldier (2021)
1 other mistake in New World Order - chronological order
Starring: Anthony Mackie, Daniel Bruhl, Sebastian Stan, Wyatt Russell
Power Broker - S1-E3
Continuity mistake: At the bar, the amount of liqueur in Falcon's snake drink increases between shots.
Bucky: I got a vibranium arm. I can take them.
Sam: And I can fly, who gives a shit? Wait.
Power Broker - S1-E3
Trivia: When Dovich and Karli are speaking in the street in Vilnius, Lithuania, visible in the background is a gate being guarded by several men, and on the gate is an encircled X, very reminiscent of the X-Men logo. The fictional nation of Madripoor seen in this episode is also closely associated with the X-Men in the comics. (00:38:57)
Question: Why does Bucky rip his jacket sleeve off before jumping out of the plane? Just for the sake of an audience reveal to demonstrate his artificial arm?
Answer: Aside from visual aesthetics and it being nice to see the metal arm. In world/practically I think (and I believe this is the reason why he tends to not have a left sleeve in most action we've seen him in prior films) it's also to assist with mobility during fights. The metal arm likely behaves a little differently than a human/bone and flesh arm does - and restricting that in a sleeve during a fight (especially in a thicker jacket sleeve) might mess with his reflexes. So removing the sleeve probably assists with the mobility of that arm.
Chosen answer: The sleeve probably would have been ripped to shreds in battle anyway. He was just saving time by ripping it himself. Also, gunfighters would take off their coats in a duel or an arm wrestler rolling up his sleeve.