A lie can travel half way around the world while the truth is still putting on its shoes.
I knew there was something wrong with Zeitgeist when I saw it pushing the 9/11 conspiracy crap, but I still was intrigued by the first religion segment. So, I investigated Zeitgeist's claims on that. It said that Krishna was a virgin birth and was crucified like Jesus. I lived in an Ashram as kid (been to India 4 times) and was taught a lot about Krishna, but I never heard that. However, I still did the research to be sure. It turns out Krishna's mom, Devaki, had several kids before him. Also, according to 2 Version's of the Mahābhārata, Krishna retired into the forest to meditate. Vyasa's Mahābhārata says that Krishna ascended to heaven and Sarala's Mahabhārata says that a hunter mistook Krishna for a deer and shot an arrow, killing him. Zeitgeist also claims Horus was a virgin birth (comparing him to Jesus) but his mother, Isis, had sex with Osiris before giving birth to Horus, who died from a scorpion and was not crucified. Zeitgeist makes many other claims about deities that simply do not match their mythical stories.
So, basically Zeitgeist just straight up lies. Maybe the film maker thinks that his mostly young hipster/hippie audience is too slack to do their own research and he can get away with it. Zeitgeist is a stylized, slickly produced piece of propaganda.
Here's a video that exposes Zeitgeist.
It's not as entertaining as Zeitgeist, and it doesn't have as good production value. However, it has something Zeitgeist does not have, substance.