for such a well engineered car its a real shame about the looks
I don't like the looks either, but that's subjective.
I would call the i3 VERY far from "well engineered". In North America, it was found that the KLE's (2nd on-board charger) were blowing and thus causing charging speed to be cut in half. Apparently it was some design flaw, so the band-aid was to reduce charging speed a bit until a redesigned part was available (took many months for that). Everyone w/the REx was getting check engine lights all over the place, and they still are. Some are spurious, others are real problems (e.g. misfires, moisture in the REx engine, camshaft-related problems IIRC, etc.) Early i3's also seemed to have body hardware issues w/false open door/hatch detections.
A couple folks have broken their motor mounts or motor mount bolts. It's not REx specific. One guy w/i3 BEV had his motor mount bolts break twice, causing major damage each time, requiring replacement of many parts and a boatload of labor. They put on a J1772 handle lock on the car but w/NO options, so the handle stays attached and locked to the car like a parasite even when charging's done. It's ok for the European charging case where you bring your own Type 2 Mennekes cable and you can unhook on the station side but it sucks for the plug sharing case in the US. (Who knows why they didn't look at how Nissan did it and provided 3 options: auto (unlock when done charging), don't lock or lock (stay attached like a parasite) when they added it on the '13 Leaf?)
The REx version seems very unreliable in general, w/all sorts of reports of check engine lights, drivetrain malfunctions (sometimes keep cropping up again, after visits to the dealer) and some restraint system errors (sometimes requiring wiring harness replacement). Some of the drivetrain malfunctions require a tow.
There are also numerous complaints of people going out to their cars finding the windows are wide open. The cause it believed to be buttons on the fob being pressed (feature to open the windows remotely) when in one's pants pockets. I believe there's nothing in the UI to disable that.
There have been a few reports of something failing (I think it was either their EME or KLE) that ends up damaging the battery pack, causing the dealer to need to replace the entire pack or all the cells.
The REx engine is too wimpy to make it up steep hills at highway speeds (not safe if you can go say under 40 mph on a 55+ mph speed limit grade). And, it's a long story about why the US version doesn't let you engage the REx engine earlier to avoid this (ala Volt's mountain mode).
A November update (
BMW i3 Software Update 15-11-502 Fixes Flaws, Adds Features) apparently has some mitigations for the broken bolt, spurious CELs and finally unlocks the handle when done, but doesn't provide options to the user.
It used to be on the i3 Facebook group, at least one new problem was reported per day, on average. It's died down a bit, but it's still about 1/day.
It also seemed dumb of them to include J1772 CCS/SAE Combo as the DC FC option for the US market when the infrastructure was almost non-existent at the time it shipped and still is far behind CHAdeMO in the US. For the Japanese market i3, they include CHAdeMO, which was likely a pragmatic decision. In the end, they ended up having to support 3 DC FC plugs, depending on the market: Combo1 (aka SAE Combo, for North America), Combo2 (for Europe) and CHAdeMO (for Japan).
It is a fairly fast vehicle in its price range though and the REx idea is a decent one. And, I applaud BMW for taking such a bold approach w/the use of CFRP but the overall execution is lacking. If the i3 qualifies at "well-engineered" then the Leaf is somewhere WAY above "well-engineered" except for battery degradation. (Despite the Leaf having been on the market for years longer and having MANY more vehicles on the road (and higher sales too), we don't see anywhere near this frequency or magnitude of problems on mynissanleaf.com or a few Leaf FB groups I'm on.)