I'm currently in the process of purchasing a BMW 320D Touring 63 plate with 88,000 miles on it's back and would like to know of any issues to watch out for 

Morning Craig

Welcome to the Forum

As with any purchase of a used car History History History and not just the service book, check the MOT history too. The advisories list tells a story about how well a car has been maintained.

Suspension bushes have a life, normally around 80 to 100k so be prepared for work that may be needed there. Also, around 80 to 100k I would expect a gearbox service to be due or evidence it's been done.

Then it's the obvious Wheels & Tyres, preferably all the same make with no signs of odd wear Body work all good, and interior clean no stains rips or tears. 

If so far so good, then test drive. A good long drive to make sure it's up to temperature no knocks clunks or rattles brakes work with no pulling or snatching. When back leave it ticking over and make sure all accessories work all lights are OK AC/Climate control is good. Then get out and check under the car and the bonnet for and leaks (remember you will get some water dripping from the AC) 

Good Luck and if it works out ENJOY

Dave