Deliberate mistake: Here, as in many other episodes, Doug and Tony are time-shifted wearing period (in this case, Viking) clothing. But they tumble into their next adventure magically wearing their left-behind 20th Century clothes again. (00:45:30)
Suggested correction: A comment, not a correction to your astute and correct observation about the Time Tunnel. Aside from it being episodic television that allows characters to look the same in all situations, I believe Tony and Doug keep their clothing, hair length, lack of facial hair, etc, because the Time Tunnel "remembered" the exact disposition of Tony and Doug when they first entered the Tunnel, allowing them to keep their clothing, hair length, etc., as they slip through time. Any "Time Tunnel" aficionados wishing to add more to this would make a fascinating discussion.
A valid speculation with which I agree, but as the poster himself points out, not a correction.
