In the title sequence, the close-up shots of Caine's arms moving into position over the cauldron show his right arm covering both the dragon AND the tiger.
In opening sequence (during pole fighting/training) a view of the surrounding hills shows a 50kV electrical tower (something that was not in China in that era).
In the title sequence the view of young Caine is looped in the pebble scene, as the smoke behind him reverses twice.
Cain frequently requests "water" when he arrives at a town or someone's one. However he's always clean shaven which is something that would require that he have access to water to be.
In the title sequence, when teenage Caine is stick-fighting with Master Po, an electrical transmission tower can be seen in the background.
In numerous episodes, the characters are wearing clothing (like shirts that button all the way down the front) which were not available during the time period when the series is set.
In the title sequence, when Master Kahn says 'pebble' his mouth says 'stone'.