Just when I had said no impact from the eLSD system, called EDLC by MINI, I believe I have encountered an issue with it.

The two most noticeable times this has happened, the car feels like it completely locks up and goes into “ice mode,” where the car would just plow straight ahead. Both times this happened, I was in a cornering situation where I needed to slow down, and it would cause severe, time-sucking understeer. The car literally felt like it was on ice, and understeered to oblivion. Posting about it on a couple car forums, I found out that this is something actually designed in by BMW as a “safety” feature. The car, often with a wheel up off the ground, cornering, may get confused with the input, think you’re trying to avoid an accident, and force you instead to plow head-on, as front end collision tends to be the safest form of collision.

Obviously, this is not desirable for autocross, and exactly the sort of thing I was worried about when deciding to add this option. However, after digging a little more into the issue, one of the top HS MINI drivers commented that the general consensus is that the car will do this when the brakes are being stabbed at. The car’s in a state with high g-forces, one rear wheel is up, and the brake gets stabbed, and the car will go into “ice mode” and plow away. I think this can be further affirmed by the fact that I’ve had three very high level drivers in the car, all of whom push the car much harder than I do, and none of whom that have run into this issue. We’ll see moving forward if I continue to run into this.

More light on the subject by someone else on the MINI forum:

A guy I know who used to work on ABS systems commented on ice mode once, it went something like:
With too rapid application of the brakes, the rears lock up before the system can do anything about it. The EBD (Electronic Brakeforce Distribution) tries to move the brake bias forward. The only thing it can do is shut off the valve supplying fluid to the rear brakes. Now most of the brake lines are shut off, the pedal instantly feels a lot harder. 
The pedal feel is what purturbs the driver, but the locked rear wheels is what causes the problems.