Revealing mistake: Kim is supposed to be hanging from the tree by the ropes around her wrists, but you can see she is standing on a platform.
Continuity mistake: The Bobby Wasabi dojo receives the amazing Punch Master Elite that is apparently not even available in stores yet, however you can see the piece of equipment in a previous episode, S2E15: A Slip Down Memory Lane. The Punch Master Elite can be spotted in the back left corner of the dojo in the first scene. Other than that you can just barely see it if you look closely into the dojo when the camera goes to that angle in the scene where Jack regains his memory and breaks the under 15 record for brick breaking. Aside from these 2 sightings, you don't see it again because it is a flashback episode, and beyond that, you actually don't see it again until S2E20 when Milton opens it as a gift from the Mayor, awarded for tremendous bravery in capturing an escaped convict.
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.