I'm sure this has been discussed before. When Vito is looking at his fish tank while Clemenza and Tessio are complaining to Michael the two start to plead with him to intervene. Vito turns to them and asks them if they're loyal and whether they trust his judgment. It would seem that only Clemenza answers. Bit of nice foreshadowing there!

And he gives Micheal a left-handed handshake!

That scene is very revealing. When Vito asks, "Do you trust my judgment?" Clemenza answers, fervently, "Always, Godfather." Tessio just hisses, "Yesssss..." And Tess gives the left-handed handshake. Treason will out!

Okay, I watched that left-handed handshake again. When Tessio stands up, he turns to his right to exit and doesn't have the intention of shaking Michael's hand. However, he apparently reconsiders and stops with his body at an angle to the desk behind which Michael sits. It is from that position that he extends his hand. It happens quickly.

I noticed that the first time I saw the movie and figured out that Tessio was the traitor. Similar device used earlier n when Luca refused to shake hands with Tatt.