Most evidence in the original series comes from Episode 10. Mimi gets upset after Koushiro ignores her when he is busy deciphering glyphs and runs off. Koushiro then uses all his skills to help her escape the labyrinth.
In Episode 14 Koushiro (and Taichi) accidentally walk in on Mimi in the bath. She throws some stuff at them.
-In "Digimon Adventure 02: Diablomon Strikes Back" ("Digimon Adventure 02: Revenge of Diaboromon" in the dub) Mimi goes to Koushirou as soon as she arrives in Japan.
In Diablomon Strikes Back movie Mimi comes to visit Koushiro. And in Digimon Tri Reunion Koushiro dresses up to try and impress Mimi.
Mishirou is one of the more popular shippings.