Well, first off, I'm gonna say that you have excellent taste. Despite what some negative people may say abot them, they are a bittersweet car...emphasis on the sweet though! I don't have a whole lot of experience on the E38's, but here is some of what I know.
Here's the bitter:
You want to watch for rough idle. Does it run nice and smooth? Or does it seem to kind of run smooth and then almost "blub bluh blub blub" then into a bit of smooth idle. (sorry, dunno how to translate sounds into text)
How does it start when it's cold? You can feel a that the car is running/idling, but it shouldn't be as rough as your Chrysler. Does it seem to want to hesitate as it is just firing?
Those are a good sign of neglected maintenance. Run away from the vehicle unless you have a cash cow and don't mind sinking it into fixing the rough idle and can get the car for VERY cheap.
Some more bitter: Though these are mostly service items and would have had to have been replaced sooner or later, depsite whether you owned the car since new or not, all of them combined can add up to quite a bit bill if you don't do your own work.
Take the car for a test drive...and not on a salesman route, on a route with a bunch of different road surfaces. Drive it in the city at the limit, drive it on the freeway at the limit and especially at around 50 mp/h (about 80 km/h) with a steady throttle to keep a constant speed. Anywhere between 45-55mp/h (70-90 km/h) the steering wheel should not have any shimmy in it (even if ever so slight). These are symptoms of the most common fault: Bad upper control arm bushings. A pig to replace if you are replacing just the bushing. It's easier if you decide to replace the whole control arm with bushing already pressed in with new balljoint.
Aside from that, check for how the tires are wearing, if they haven't been replaced for the sale. With the 'iL' versions of these cars, they usually have a self leving rear suspension. Now on the E38's, I don't know if they are hydrolic or not, but if they are, check to see that there is not leaking coming from the rear shocks...a very expensive part to replace is they are leaking.
I do encourage you to see if the car will come with a warranty and a money back guarantee. And remember, just because you might have one bad experience with a 7-series BMW, doesn't make all of them horrible cars to own. Keep on top of your maintenance, and these cars will see 300,000+ miles no problem.
And I put a lot of emphasis on not buying the first 740iL you see. I looked for almost 6-8 months at about 100 different 7-series before I bought mine. You don't have to wait that long, but my point is look to see what is out there, the differences, what needs what, and when you do find the one that is in perfect condition, you won't regret waiting!
Now here's the sweet:
I don't believe I have been able to express words how beautiful my 1990 750iL is to drive...it is something you must truly feel for yourself. With all the toys and gadget's and gizmo's, these cars are truly a mans dream!