Are we supposed to sympathize with Paradox or not? While his goal seems noble (after all, he comes from a future ruined beyond recognition and he intends to save the world from destruction), he does rather monstrous things in order to achieve that goal, including heavily damaging Judai and killing a lot of innocents, as well as Pegasus and Sugoroku.
Are we sure that the protagonists do the right thing? Does killing a person who intends to avert an utterly ruined future solve everything? Do people truly have the power to change the future?
Ass Pull: Since it's Yu-Gi-Oh!, of course. The three protagonist draw the perfect cards in their first turn to win the duel. The worst example is that the three last cards they played are obviously designed for the final turn. Yugi and Judai have two Trap Cards with similar names and basically the same effect just to buff Yusei's Stardust Dragon. And Yusei's Trap Card Stardust Mirage allows him to revive all of their monsters that are destroyed in the during turn, but it requires Stardust Dragon on the field. However, Stardust Dragon was stolen at the beginning of the movie. There is no way that Yusei could predict to get his card back. Also, it only works because of violation of the rulesnote Yusei activated Stardust Dragon's effect. It should be revived on Paradox' field, but it doesn't and it shouldn't even be able to be revived in the first place, since it wasn't Synchro Summoned.
Epileptic Trees: The movie had a good share of those until it came out. Now there are theories about how the movie is connected to 5D's, the movie's loose ends, including Paradox's backstory and identity.
The loose ends and Paradox's backstory had some light shed on them in Episode 135 of 5D's.
Hilarious in Hindsight: It has been stated in the Gospel of Truth that Pegasus' least favorite food is squid. And now in the movie, someone with hair resembling a squid is out to kill him. Least favorite food, indeed.
Ho Yay: Johan isn't even present and only mentioned once, but the producers still somehow manage to make the impression that there is something between Judai and him. Judai is practically furious when Paradox plays Rainbow Dragon, while he made no such outburst when Paradox played Sho's Cyber End Dragon the turn before.
In the Sakiyomi JumBANG! broadcast promoting the movie, Paradox hacks the broadcast and tells the cast to find Stardust Dragon. The three members search all over the theme park the broadcast takes place at. At the end, Paradox mocks them and tells them they'll have to wait for the movie's debut instead. Cue much rage from Zaripai.
With Paradox's hair resembling a squid, the fandom is joking around with "an epic battle between marine invertebrates" - starfish for Yugi, jellyfish for Judai and crab for Yusei.
People enjoy making Paradox say "YA-HA!" in fan material thanks to him and Hiruma sharing voice actors.
Judai's salute pose.
Chest spikes. Oh boy.
Yusei's distorted face (which can be seen well during a freeze frame) as he is knocked back by Paradox's attacks gained a slight popularity in fanart.
Nightmare Fuel: Paradox's fusion with Sin Truth Dragon. To elaborate, Paradox is clearly in pain when he pays his Life Point cost for the monster's summoning (explaining that he sacrifices his body in doing so), his eyes temporarily go blank during the fusion, and the next thing we see is a close-up of Paradox's veiny, angry face. He also makes Dark Marik-esque faces at the protagonists afterwards.
Also, The destroyed world.
So Bad, It's Good: For some people, the epic cheesiness of the dub saves the dub version from being a bad film.
What an Idiot: Why didn't Judai activate his Neos Spiral Force to buff Yugi's Dark Magician when it's attacked by Paradox' Malific Blue-Eyes White Dragon? Because the duel would be over, but the Spotlight-Stealing Squad is Yusei, so he deserves the buff.