Yomigaere! Eiyuu Densetsu - S1-E1
Character mistake: Not to dispute physics in an anime about people drawing arcane cosmic powers from constellations, but when Marin explains to Seiya what happens when you shatter a rock into smaller pebbles, she says that you "destroy its atoms." That's not how physics works and luckily for her, Seiya and everyone else in Greece at the time, she did not create a nuclear fission in the palm of her hand just to prove her point.
Doragon! Muteki no ken to tate - S1-E4
Character mistake: The announces during the fight says that the tournament is "down to 10 Saints", but 10 was the starting number, 3 have been already eliminated. (00:04:30)
Doragon! Muteki no ken to tate - S1-E4
Character mistake: Shun says explicitly that a Saint's body is no different from any ordinary human's. That's quite funny, considering that in the previous episode Hyoga fought creating temperatures of -100 °C (consistently, to defend himself, and aggressively to freeze Ichi), which would have messed up really badly both contestants.
Fenikkusu! Jigoku o mita senshi - S1-E6
Character mistake: When Jabu gets maimed by the Nebula Chain attacking from above, the commentator says "One point for Andromeda Shun." Points? There never were points during the previous fights. (00:11:05)
Taose! Ankoku Phoenix gundan - S1-E8
Character mistake: In the sequence with Ikki's Shadows jumping over the lifting bridge, the first one is not wearing the visor they all have to wear. (00:05:00)
Kyoteki! Ankoku shiten oh arawaru - S1-E9
Character mistake: When Black Dragon visualizes himself dealing a mighty blow to Shiryu, the Bronze Saint is wearing two Dragon Shields instead of one. (00:22:10)
Shito! Kyofu no kokushiken - S1-E11
Character mistake: Kiki says "Oh! He stopped bleeding" when he is in fact still bleeding from the other wrist. (00:10:35)