Fortunately, this particular one is nothing major, so you don't have to worry about your save file being corrupted or the latest update for the game bricking your system. The YouTube upload above shows a match between Terry and the Ice Climbers on the Dream Land N64 level.
The match plays out as normal until around the 40-second mark of the recording, when Popo and Terry are frozen in time. As you can see, Nana is horrified and does her best to interact with the two fighters locked in battle, until she gives up and jumps off the stage to end the match. It results in Terry winning.
This appears to be an isolated case at the moment, but it's definitely a glitch Nintendo will want to patch out.