Greetings - I've had a client inquire about 360 video shot inside a moving car.
Aside from possible issues with rolling shutter (that seem, after reading through the forums a bit, to be manageable if the head is mounted on an angle) I also anticipate issues with parallax problems. If I'm mounting over the passenger car seat, there's going to be a lot of interest in what's happening inside the car.
How poorly will the vehicle innards look in everyone's estimation? Would one of the Go-Pro mounts, like an inclined Freedom 360 with 5th camera, or just the H3Pro6N (and we patch the nadir) be able to provide decent interior coverage of the vehicle?
I would definitely go for a Freedom360 mount in standard configuration (6 cameras), while orienting the F360 in a way that no important parts are across a seam, or at least not cutting across some unstitchable/unrepairable areas. depending on the bumpiness of the ride, you can get really creative with a monopod, clamps and sandbags. or you can consider suction mounts (see http://freedom360.us/shop/tri-base-suction-cup-mount/) which will attach to the side window, or the sunroof, in 5x flat or in 6x configuration with a short pole. if you want to get more elaborate, you can use suction cup mounts on the outside of the car, and use something like the manfrotto dado system to get the F360 inside the car where you want it. this will eliminate the problem of masking out the support other than the pole.
Rolling shutter is only a problem when it is very very bright outside, some clouds help a lot to bring down the problem. given the problems the gopro cameras have in low light (especially dark car interiors), it doesn't hurt to add a bit extra light inside the car (i.e. LED strips with proper color in strategic hidden locations).
In regards to stitching, as Alexandre already pointed out, you need to make compromises: "perfect" is unattainable in this context, "good enough" is a better goal. it always comes down to the quality of the control points, and the resulting optimization in APG. In order to help with CPs, I would consider to place temporary markers on all surfaces that will not have CPs as well as flooding the car interior with light in the beginning of the take, and then remove the markers and the flood light, and continue with the actual scene. I would experiment with different setups, and shoot simply sets of jpgs for each, and do a quick stitch, and see if you like the result.