Yeah, I looked at the arithmetic and yeah, the arithmetic is sketchy (if 22% cells aren't already sketchy for that price). But yes, they do cover the doors, the rear, basically all non-transparent surfaces with cells. Other neglected things are what happens if you park under trees, in a forest of tall buildings, in parking garages. It's never going to be 7.5 m^2 x 0.22 x whatever you want to claim for mean daily integrated flux through a perpendicular surface (200 to 300 W/m^2 if I recall correctly).
It's also not clear how much of a "real car" they have in mind. Is it an ELF http://organictransit.com/ with solar cells on all surfaces? The ELF now looks more like a car with glossy hard sides than it used to, and they now seem to come with a 100W solar panel on the roof, allowing one to accumulate as much as a KW-H over a whole day. Since it comes with a 500+ W-H battery, it actually could fully recharge over a day in the sun. This gives it a range of around 15 to 18 miles no pedalling on flat ground. Obviously if you add battery, you can add range, but you probably can't fully recharge with only sun unless you add more panels.
The ELF is not vaporware -- I live in Durham and see these all the time on the roads (they cost $6000 to $9000 depending on how tricked out you get them). Adding solar capacity is actually pretty easy, as is adding battery capacity. One could probably accessorize to 30 miles a day and still manage a full recharge on its rated mileage of 34 mpkwh (add another 500 W-H battery and another 100 W panel with some sort of hinge that you can tilt up to horizontal-ish when you park). Actually, this isn't bad at all, and would probably do me just fine on my commute, leaves the money in my home town, and gives me the option of pedalling to get SOME exercise on the run without having to pedal up all the hills on muscle alone (hot and sweaty, at least, during the summer). Pedalling also extends the range, obviously.
The catch is that it isn't technically a car, and cannot go 45 to 50 mph on the one road I would HAVE to drive on that is 45 to 50 mph if you want to go WITH the traffic, and it is even more of a road obstacle than a bike if you are traveling under road speed. Which makes it still quite dangerous, although maybe a hair less so than a bike (at least one person I know of has been killed on the road I have to ride in on in the last year on a bike).
So, can one imagine taking the working ELF design, bumping its internal energy storage to 14.5 KW-H, bumping its solar capacity to (say) 400 to 600 W, (say, 2400 KW-H/day) increasing its top speed to street legal (say 55 mph for mostly in town driving), sticking with polycarbonate sides but increasing seating to four in more of a car-like configuration, and still maintaining at least 12 m/KWH, needed to get 30 m in a day's charge (with no pedals)?
It's not completely insane. Doubling speed increases power required by around a factor of 8 but takes only 1/2 the time to go the distance, so it needs 4 times as much energy IF one assumes energy is dominated at that point by quadratic drag. Well, we've quadrupled incoming power (relative to 30 miles/day), increased stored power by a much larger factor than necessary, so in principle if we haven't added TOO much weight or MUCH less efficient motors, we are at least in the ballpark. Can we do this by no more than doubling the high end cost? Again, maybe, hard to say. We'd save some by not having pedals and all the dual power source gearing, we'd spend it and more on the extra batteries, solar capacity, and the 4+x more powerful motor. But it might be doable. ELF might make it there on its own as it has the substantial advantage of building and selling actual vehicles right now that already work pretty well as in-town commuters, better/safer where the speed limit is 35 mph and under, not so well where it is 35 mph and over. If they are and remain profitable as they grow, they could end up bringing out higher end, closer to car vehicles within a year or two even without any competitive incentive, and in Europe the cost profile may or may not be advantageous for a local competitor to develop.
ANY real improvement in several critical components -- motor efficiency, energy recovery while braking, active solar charging, energy storage -- could make this general approach into a COST efficient alternative to auto-based in-town or in-city commuting. Cheaper than a car, check. Self-solar-fueling or nearly so for the expected daily driving range, check. Low maintenance (compared to a car!), probably check. Made of materials that will last without rusting out or getting brittle (and cheap to replace), maybe check, dunno. Insurance? Dunno. Safe? Probably not as safe as a car, conceivably safer than a bike (if they build them truly street-legal at 55 mph). Quite aside from "saving the planet for the whales", I've thought about them as ways of saving the $100-150 I have to spend per week on fuel, maintenance, insurance, and depreciation to do my daily commute in a car whose capital cost was over $16K used. Spend less than $16K new, save (say) $1200/year, and be insulated from fuel supply chain interruptions and price hikes? Sounds like a good bet to me, if it is safe enough to drive without quadrupling the risk of an accident during rush hour.