Re. the tyre skipping, when I turn out of my drive at low speed (nearly on lock) I can feel one of the tyres slip/skip (I assume the outer side) in my GS-250.
No battery weight in the back. I did wonder if the tyres were getting past it, they are a good brand (Continental I think), but probably 50-75% worn and may have gone a bit hard, especially in this colder weather.
A quick Google reveals issues with Mercedes and Jaguar too. Also an issue on the Lexus IS, from another forum:
"I had the same problem and when i mentioned it to the dealer at its last service he explained the same reason - the front wheels tilt when on full lock and it is the tyre struggling to grip at that angle. nothing to worry about and not dangerous, they all do that. "