Pah. The whole thing falls apart when you remember that Yoda was working with Palpatine to destroy the Republic.
It was Yoda who sent the Jedi knights (the double-0's of Star Wars) into a stand-up battle where they all got slaughtered. Only Mace Windu disobeyed to do the sneaky thing Jedi are so good at, and almost won the whole battle right there. If only someone had gone with him, it might all have been different.
Then, at just that moment, it turns out that there's a new army the Republic can use, to replace the one Yoda just threw away. And the people who built that army seem to think that it was Yoda who commissioned it. Which happened on a planet that someone managed to delete from the Jedi archives. You think they let Palpatine go snooping around in there?
Obi-Wan (the only other Jedi to survive the meat grinder, who relied on Yoda more and more after Qi-Gonn's death) hides Anakin's son in a fiendishly clever place: Anakin's home town of Mos Espa, Tattouine. In the care of Anakin's brother (half-brother, I suppose), Owen Skywalker. With everyone knowing that he's Anakin's son. Hardly an attempt to keep him safe, I'm sure you'll agree.
And then he (and Yoda, later) continually lies to Luke about the relationship between Vader and Anakin. Which gives Vader the perfect opening when the truth is sprung on him in the middle of battle. Leah was just a girl, and therefore could be more easily ignored.
Once Obi-Wan dies, and the rebellion begins in earnest, Yoda summons Luke to him to keep the one force-sensitive person around out of the field of battle under the guise of training him. Again, he lies to Luke about his ability in an attempt to keep him away from Bespin. Because without Luke, the rebellion would have been crushed there, and the Galactic Empire could have continued unopposed.
It's also interesting to note what happens to the Jedi conspirators when they die: Unlike any of the other Jedi we see (such as Qi-Gonn), their bodies just disappear and they become part of The Force. Palpatine doesn't seem to know this trick, though he offers to teach it to Anakin, to win him over. Is this some secret teaching Yoda discovered to prevent his Jedi agents being uncovered in compromising situations? It wouldn't do, after all, if the Jedi Council found out that Jango Fett had been acting as Yoda's catspaw on Kamino.