Chris Urmson doesn't think it's funny, but he can't help but chuckle when he talks about some of the things he and his team have seen while logging more than a million miles in Google's autonomous-drive vehicles.

"Every once in a while it's shocking what we've seen people doing," said Urmson, director of Google's self-driving car project. "The way they operate their vehicles is worse than we expected."

In one case, he saw a woman eating a bowl of cereal while driving. "I could see the milk dripping off the spoon," he said.

Urmson spoke to CNBC as the technology giant begins its next phase of research into autonomous-drive vehicles.

During this phase, a fleet of Google cars will move from the test track and onto the streets of Mountain View, California. And to better understand what the public thinks about sharing the road with these vehicles, the company has set up a website to get feedback from people living in and around the city.

"We want to understand what is beneficial or frustrating about having these vehicles in the community," Urmson said.

Public fascination—and to some degree, skepticism—with autonomous-drive cars has increased recently, following reports of a dozen minor accidents involving Google cars over the last six years.

Two of those accidents happened earlier this month. Google said the low-speed collisions happened when its cars, stopped at intersections and were rear-ended by drivers not paying attention.

"In both cases we were stopped for a number of seconds and then somebody rolled into us," he said.

So far Google, which will release monthly data on accidents, says the collisions have been caused by the other drivers. But Consumer Watchdog has called on the company to disclose additional information, saying that "Google is dribbling out bits [of] information in the hope to silence legitimate calls for full transparency."

"They are testing on public roads and the public has a right to know exactly what happened when something goes wrong," the organization said.

Urmson said the Google team has seen its fair share of questionable—and sometimes flat-out dangerous—behaviors by other drivers and pedestrians.

That includes seeing two cars head down the wrong side of the road, against traffic, then wait to turn at a stoplight as if they were in the proper turn lane.

"[Drivers] put their attention elsewhere and that's when they make mistakes," Urmson said.