Did Zetsu know about Tobi's truth/identity all the time? I'm guessing Zetsu is one of 


   Madara Uchiha's successful projects (created from First Hokage's DNA)! 


And that makes me believe that 


   Obito and Zetsu must be knowing each other!


But on the contrary! When Tobi was searching Sasori's ring (after his fight with Chiyo and Sakura), if you observe Black Zetsu and White Zetsu's comments on Tobi, one would think that they weren't aware of Tobi's serious part of life.
Zetsu did know Tobi from the beginning.


   Tobi has interacted with the White Zetsu the moment he arrived to Madara's cave. Black Zetsu was created by Madara in Obito's presence.


The reason for Zetsu supposedly not knowing Tobi could be


He wanted to keep it hidden from the other Akatsuki members.
Kishimoto haven't thought about it at the time.