Only fixing one tire...?
 

I have one flat that cannot be repaired (sidewall damage). My original plan was to replace a pair of tires, but now I am probably only going to replace one tire. This will leave me with 3 Bridgestone Potenza RE01Rs and the last tire a random brand (used).

If I go this route, will I encounter any issues with traction control? Also, would I cause any damage to the LSD/transmission by rotating the unmatched pair to the rear?

Thanks,
FS

Ideally you would place the different tire in the front, as two different tires (each with different amounts of wear) would put some stress on the diff

Match the replacement tire to the ones you already have and put them on the front axle. If you have significant wear on your current 3 good tires (more than 50%) I would recommend two tires.

Look for a used same tire.......or replace 2 same.......used or new

Don't throw a random oddball into a mix of 3...you are asking for it..especially when it is cold