Well anything except forget to mention they just swapped wheels and tires on the car, and are now running on a 195 front - 345 rear tire(OK that's over dramatic). I see this and then get irritated. I shouldn't care, not my car, but I do try and point out to them, that the overall tire height is causing the problem. Normally get the argument back that so and so said it would be ok, or blah blah blah. It can and possibly will damage the Fwd clutch/transfercase and possibly the whole transmission, so FIX it, by swapping tires. I highly recommend not driving a vehicle in this condition.
Here is how troubleshooting a problem works. Identify problem. Did it exist previous? Changes before problem? Put it back the way it was, did it fix it?
So the problem or the great part is that the GT-R is all wheel drive. It has a series of clutches/differentials in the car that help to transmit power between the front and rear wheels. In the R35 its in the GR6 transmisserdiffercase, and its called the FWD clutch, but I would call it a transfer case. It has an input and output. The input is from the transmission, and the output goes to the front wheels. However it is mechanically coupled to the front wheels though the front driveshaft, so both sides are always spinning. When the ATTESA system decides it needs more front torque, it locks up the clutches in the transfer, and sends some power to the front wheels. The magic of all wheel drive.
When you have tires of different heights... Now that is key. Height. The overall rolling diameter. Not 305. Not 30. Not 20 inches. The height of the tire. You need to check with the manufacturer of the tire,find it on Google, Tire Rack, the interwebs, or get out a damn tape measure and measure it. If you are more than about 12 mm difference in overall height in a GT-R, you will probably have a problem. 0-4 mm is good. 4-8 mm is acceptable. 8-12 mm is iffy. 12 mm plus will probably set a light. Stock is 0.1 inch or about 2.5 mm.
Stock GT-R Wheels (2009-2012)
Front 20 x 9.5 45 offset
Rear 20 x 10.5 25 offset
255/40/20 Front 28” diameter
285/35/20 Rear 27.9” diameter
What have people put on the car? Tons of different sizes. Square - 285 all around, 275/315. 275 square. Check out this whole post on GT-R wheel and tire sizes.
I know this can be an issue because I have burned up ATTESA transfer cases in R33 GT-R's. I was stupid, I didn't listen to people that knew better. Don't be stupid. Do the math, figure it out before you go just throwing the latest greatest hellaflush bullshit on your GT-R.