Excellent move having the mechanic check it out. They've pretty much ironed out most of the problems by 2000 but there are still issues with them. I don't have direct experience with the e38 but gave serious thought a year ago to replacing/supplementing my e32 with an e39 540i & spent lots of time familiarizing myself with various issues.
A few that come to mind are:
1. Radiator -- plastic necks break off unexpectedly. Automatically replace it by 50k or 60k miles
2. Aux. fan failures
3. Pixel dropouts on the dash display -- sometimes the dealer will cover the replacement part if you cover the token labor charge, depends on the dealer.
You probably know that it is a close cousin to the 540i, here's a good link for them:
http://www.540i6.com/links.html
There was an engine mod I believe mid-year 2000 where it went from single vanos to dual vanos, where "vanos" is the variable cam timing. 97-98 were non-vanos. Single vanos was introduced in 99 on the intake valves. Intake & exhaust dual vanos introduced in mid-2000. They all have the same basic shortblock with the design changes in the heads & intake manifold. All 97 & newer V-8's have the Alusil block & are no longer plagued by problems with the e32/e34 pre-96 Nikasil block, so no worries for you with an e38. Check the build date or check with the mechanic to find out if it has single or dual vanos, being a 2000, it could have either. Dual vanos has a higher power output & a little better low end torque.
I think the e38 still has the same automatic trans as its e32 predicessor. I'm not sure if they corrected the hesitation going into reverse, but that can be fixed relatively inexpensively by doing a mod to the valve body. Aside from that, do a drain & fill of the "lifetime" fluid & filter sometime before 100k. Use only the proprietary Shell trans fluid & use the BMW OE filter.
The control arm issues common to e32/e34's are much improved with beefier components. You might drop "Q" an e-mail, he frequents the roadfly e32, e34, & e38 forums & has an e38 & has lots of resources he could recommend.