DY: I don’t think I agree that we believe Rishonim can’t make mistakes. We believe that it’s dumb to think we can catch them because they knew a ton more than us and that if/when they did make mistakes, people in the centuries between them and now would have and did catch them. Those that made it into our corpus of Rishonim are those that knew so much that they (almost) never made mistakes. That’s why they are Rishonim.
(As an aside, I knew a massive Talmid Chacham who was once approached with a manuscript from a Talmid of a Rishon-I think it was the Rashba-and asked to help edit it for publication. He looked through it and said that there was a reason it had only been a manuscript until then; the whole thing was Naarishkeit. This Talmid wasn’t one of the Rishonim because his writings weren’t good enough to be one of the Rishonim. The person with the manuscript called this Talmid Chacham an Apikores for arguing with a Rishon and went on to find other Talmidei Chachamim who would help with his project. After 4 or 5 similar answers, he finally got the point.)
I won’t say the Ri made a mistake because I am far from knowledgeable to ever say such a thing, and 2 days is far too short to ever say such a thing. If I knew Kol HaTorah Kullah and couldn’t answer this Kashya for 60 years, then maybe I’d begin to entertain the possibility that the Ri gave an impossible example.
Oh, and I think it’s in the Shmoneh P’rakim.