Continuity mistake: When Jack is talking to Kim after he defeats the impostor, in one shot you can see the actor who played the impostor appear over Jack's shoulder; he's just standing there watching the rest of the scene.
Continuity mistake: The lockers in the Bobby Wasabi dojo change from blue to green in the same episode.
Answer: It depends. If you watch the action scenes in slow motion, you can often tell if it's the actor or a stunt double. Leo Howard seems to do a lot of his own fight scenes and acrobatics while many of the fights and flips by other characters are done by doubles; although occasionally Olivia Holt will perform a simple flip or fight.
Both Leo Howard and Olivia Holt have black belts and completed their own stunts.