there is a dmf, unless you get an auto, they arent known for failjng like most of the later fwd cars though.
they run a vp37 pump much like all the early tdi vw's, electronically controlled mechanical pump, fly by wire pedal, only thing to look for on them is pump seals leaking, a tenner for a seal kit and some faffing will fix it.
I'd be wary of any with tuning bodges, they can be chipped though, improved mpg in an auto as it didnt have to shift down to hold pace.
mpg from mine as a poorly auto was mid 30's commuting, will crack into the 50's on the motorway, hoping its improved now i have converted to manual.
the auto boxes arent the greatest, bmw stated they were sealed for life, zf say they certainly aren't, mine was playing up at 74k having been a london car for years, most get to 100k before playing up, so budget in an oil change andand filters if you get an auto.
the rest is typical E34 fare, avoid sunroofs if you can, the sills are more likely to rot on them.
I owned an e34 TD a few years ago. MPG on the autos is pretty poor for a diesel so I wouldn't expect much over low 30s unless you're doing lots of motorway miles. I found myself wishing I had the intercooled TDS - more powerful, and more tuneable. As Welshpug said, the VP37 pump is fly-by-wire. I'll add that the throttle position sensor inside the pump can give problems as the track wears and it doesn't sense where the pedal is. Used to happen on mine and my current e39 TDS has the odd hiccup with it sometimes too. The TD came with the GM 4L30E auto gearbox which is a bit fragile compared to the ZF box in the TDS. It's what killed mine in the end.
My e39 525TDS touring is livelier in comparison to the TD. It's a manual so the MPG figures are better, but not a patch on newer diesels. The looks aren't (in my opinion) as handsome as the e34 but still not a bad looking motor.
There is an O ring seal on the lift pump in the tank that can fail too which will cause the engine to cut out under about 1/4 tank, happened to me on a donor 525tds I bought (luckily within rolling distance of a fuel station!)
Was a pretty nice car to drive I thought once warmed up, even if mine was a bit of a dog (only wanted the interior).
As welshpug says, rust can be a killer on all E34s, if its a later car with the plastic sill covers they can trap a lot of mud in and rust the sills away.
Watch for steering shimmy around 60-65mph, can be a pretty common issue due to the amount of links and bushings in the front suspension
Nice bonus of the fly by wire throttle in the diesels is that if you can find a cruise control stalk, I believe its a plug and play upgrade