The most obvious continuity error from Season One, to me, has to be Twilight being surprised that Luna is Celestia's sister at the end of Episode 2 even though she knew the whole Nightmare Moon story from the book that she read in the opening of Episode 1. Then, of course, you have the rapid season changes with it being Autumn in Episode 4, Winter in Episode 11, and then Autumn again in Episode 13. There is the technological disconnect between the horse-drawn locomotive in "Over a Barrel" and the steam-powered locomotive in the entire rest of the series. Of course, if we include Season Two, the technology is so wildly inconsistent that you have lanterns powered by fireflies Flintstones-style in the very same episode that you have a hospital full of electric lights. Honestly, once Season Two started, all continuity started becoming more of a suggestion than a rule. "It's About Time" is a closed-loop paradox. The lore in "Family Appreciation Day" clearly contradicts "Winter Wrap-Up." There is Luna in "Lesson Zero" suddenly talking like she is at Ren Fest despite having sounded entirely contemporary both as Nightmare Moon and as Woona. Maybe the most famous continuity error on the show is Bon Bon/Sweetie Drops' voice being completely different every single time that she appeared during the show's run.
Now, if you are going to count animation errors or reusing assets in the background, we will be at it all day. You mentioned "Show Stoppers," which has a few examples, like Sweetie Belle having orange eyes in one scene and the crowd of recycled characters at the talent show. On the flip side, I don't think Rainbow Dash meeting Scootaloo at the talent show counts as a continuity error. She was probably just there because it was a talent show for kindergartners, and Rainbow Dash is an incredible pedo.