I haven't watched the whole thing, but I saw part of it and can vouch for their general argument.
When BMW claimed that their i3 would produce 30% less CO2 over it's lifetime than a similarly-sized diesel car, they forgot to mention that compressed natural gas cars already do that while also delivering some of the emissions benefits of fully electric cars (since methane burns cleaner). When they claimed that it would produce 50% less CO2 when powered from wind or solar, they didn't include the CO2 footprint of the infrastructure needed to support that. They also took credit for using recycled aluminum, but almost all aluminum is already recycled. (See the arguments for favoring post-consumer recycled material to understand why that matters. They're just displacing other users of the same 'clean' resources, not increasing the amount of clean raw material available.)
Tesla has never provided that type of estimate, despite benefiting from $300,000,000 in federal and state subsidies in the US alone. They also haven't cooperated with any of the third party studies. One of the most-cited studies was by VUB University in Belgium, which has conflict of interest because they sell consulting services to electric car manufacturers. The other high-profile study was written by a team that had no manufacturing expertise,, and was consequently unqualified to estimate the energy needed to make the car.