Hi Harry,
Surprised you haven't had a response yet. . . .maybe because there is lots that can be written about just what to look for - where to start!?
There are excellent write ups regarding the Zed and what to watch out for on the post called Forum F A Q . Click on the Forum option on the dark red bar above left - then look for the E85/E86 discussion option - click on that and you'll find the F A Q post. It will give you lots of information and follow ups.
The Zed 3.0i which you are hoping to look at is said to be a good match with an auto. Those that have owned them have been very positive. I have followed one on the National and a great compliment to the driver - I was surprised to find he was driving an auto - very impressive.
Generally the pre facelift (pre 2006) Zed is said to have a strong engine that is good for many thousands of miles when cared for and serviced well. Your issue will be whether the Zed has had time prompted servicing (say every 2 years or 18 months) rather than the mileage servicing which is the norm. These Zeds have surprisingly long service intervals (16K+) and so servicing may be scarce on the low mileage Zed you're looking at. Most owners would like to see regular oil changes and brake fluid changes every two years at least even with the low mileage. There are two types of services called Inspection 1 and Inspection 2 - you may find the low mileage Zed you're looking at may not have had an Inspection 2 service yet. It is more expensive than the basic Inspection 1 (mainly oil change). Costs can be kept down by using a good independent rather than a dealership garage for servicing. My 3.0si Sport (2008) hasn't had an Inspection 2 yet and it's on 57,000 miles. Bought as an Authorised Used Car from BMW in Jan and they said they wouldn't give it an Inspection 2 as part of the deal because it didn't need it yet!
The roof motor can stop working due to water drowning it - an expensive fix so check it works or see if it has had a replacement. (From £550 - £1000+ depending where fixed!)
Springs tend to snap - easy and fairly cheap fix at the rear a little more involved and costly at the front.
The car your looking at will have the usual age related issues so check it as you would any other 'older' vehicle - tyres, brakes, bodywork - accident damage via panel gaps)seat bolsters (on drivers side - they all wear).
It is also likely to have upgraded or optional extras fitted. depends what is important to you - some have sports seats fitted, different alloys (stay at 18 inch max as 19+ can crack on our terrible roads (unless you like the looks!)), different headlights, xenons, updated bumpers front and rear, aux outlet, cruise control etc.
Owners have had non run flats on front or back and run-flats on the other BUT obviously not to be mixed on the same axle. I think most would get the car on all the same tyres asap. I did what you mention with my first Zed until the rear tyres needed replacement.
A well cared for and serviced Zed will be a great investment and very enjoyable on the road.
Keep reading as there's more to learn and know. . . .and lots of knowledge on this forum.
then my thoughts would be more on the car itself with condition , number of owner's , does the MOT history stack up ? & one of my favourite's when buying private which is worth more to me than any dealer stamps 