In the first episode of GX Yugi gives the Winged-Kuriboh card to Jaden for apparently no good reason besides "to create a legacy from Yugi to Jaden". Since this movie is CANON in both series, it means that Paradox was inadvertantly the secret to Jaden's success in GX by giving Yugi a reason to make that card a gift. Explanation: For Yugi, this is his first time meeting Jaden. For Jaden, it's the third. During the duel with Paradox, Yugi sees Jaden play Flute of Summoning Kuribo, a card that is thematically inappropriate for his Elemental Hero deck, but which saves their butts. During their Crash into Hello at Duel Academy in GX episode 1 (Yugi's 3rd meeting, Jaden's 1st), Yugi insures his own past by giving him Winged Kuriboh, which Jaden of course puts in his deck, being as it was a gift from the King of Games himself, along with support cards, like Flute. Not only did this ensure Jaden's survival (note how many times in the series Winged Kuriboh has saved him), it ensured that the protagonists would have it to be saved by in that Yugi's past. If Paradox hadn't started the duel, Yugi would've had no reason to give that card to Jaden. Thus, Paradox sowed the seeds of his own defeat before the duel even began. Note: Subjectively speaking, Yugi met Jaden in this order:
episode 180 of GX
episode 1 of GX
Jaden met Yugi in this order: in episode 1 of GX, 2) episode 180 of GX, and 3) vs. Paradox.
Just a little [Fridge Horror] to note: In the duel, Papadox uses evil versions of Blue Eyes White Dragon and Red Eyes Black Dragon. Who uses those cards the most? Joey and Kaiba. Why are neither of them mentioned in the movie? Because Paradox had already gone back in time to before he attacked Yugi and presumably killed Kaiba and Joey for their cards.
Itīs not just Joey and Kaiba, he also used evil Cyber End Dragon and Rainbow Dragon, meaning he may have gotten to Zane and Jesse too, he only dueled the heroes of their series, but that's as far as he needed to go, since of the three series, the only ones left standing would be Jack, Crow and Akiza (and maybe Chazz and Aster).
Most people would think that it doesn't make sense why Neos and the rest of Jaden and Yusei's cards returned to normal after they saved Yugi and jumped back in time to before Paradox killed Pegasus. However, it makes sense when you realize that they traveled back in time to a point before history changed. And because they were at that point, history was flowing normally and their cards had the possibility of being made, so they returned to normal.
Since Paradox is implied to have destroyed Domino City completely, that would mean that not only did Yugi's Grandpa die, but EVERY SINGLE ONE OF HIS FRIENDS as well.
Judai summons Elemental HERO Neos in Defense Mode to protect himself from Paradox's Rainbow Dragon's attack. Neos has only 2000 DEF, but Rainbow Dragon has 4000 ATK. For some reason it works. And then Paradox attacks him with Stardust Dragon (2500 ATK), which is much weaker than the former dragon, yet the attack is successful.