The 1960 Corvair suspension design (swing axle) is shared with many older European cars, the most popular being the VW Beetle (with which it also shared the rear engine position). It was no more unsafe than most other cars on the road, and Nader is generally considered to be incorrect on this specific point in the book.
I can't speak to the rest, as that is the point that I'm most familiar with.
Also, the second generation Corvair is one of the most beautiful cars ever built IMO [0], and shares it's suspension design with the Corvette (unequal A-Arms at all four corners). Interestingly it's design study is what was used to do the first generation Camaro/Firebird as GM had nothing ready to compete with the Mustang.
To get even more interesting about the Corvair (I grew up around someone who had 12+ of them...): the engine is one of only three families that spins "backwards": The Corvair, The Renault (correction from comment: Citroën!) 2CV, and the Honda D/B/H series. This was due to the transmission being a standard GM transmission thrown in a different case with the rearend attached, and a jackshaft going back to the engine, making the reverse rotation necessary. A couple of people have actually installed Honda B series engines on these [1], which surprisingly works quite well on the old transmission since they make little torque and rev very high. It's also why there were kits to put a V8 in the back seat by removing the jackshaft and mounting it to the normal GM transmission input.
[0]: https://www.hotrod.com/uploads/sites/21/2012/03/hrdp-1202-19...