There appears to be a mechanical issue.
This year's Goodwood Festival Speed was full of amazing sights, and brilliant videos from the event have continued to arrive even after the festival's end. As an example, check out this clip of a Jaguar F-Type coupe completing the hill climb on two wheels. By the end of the run, the car probably should visit a mechanic.
Driver Terry Grant uses a ramp for help getting the F-Type onto two wheels, and he manages to balance the tyres on a knife's edge during the entire drive up the hill. There are a few times where the car seems to be very close to tipping, but Grant never lets the Jag drop.
Problems arise for the Jag at around the two-minute mark of this video, though. At first, the only visible sign of this issue is smoke coming from the rear end. At 2:47 things get much worse when a plume of smoke puffs out of the car. The view from underneath suggests that the rear differential is the source of the smokescreen.
In all likelihood, Jaguar's designers never intended the rear differential to operate on its side for so long. The lubrication probably doesn't have an even distribution, which is allowing part of the component to overheat. At the end of the clip, there's another massive plume of smoke that might result from the fluid hitting the overheated section of the differential.
Jaguar is currently preparing a refresh for the F-Type that appears to give the model a completely different look at the front. There are rumours that BMW's 4.4-litre twin-turbo V8 could replace the existing 5.0-litre supercharged powerplant.