As of last night, my 2000 323i (70k miles) started making a knocking sound directly below the shifter. It's not really audible from outside the car, and is only happening when the car is in a low gear or is moving VERY slowly. The knock speeds-up in frequence the faster the car is going until it doesn't seem to make any more sound.

I just had Inspection 2 which included an Engine Oil Service at the dealership last week. Perhaps unrelated is my MPG status: it's gone down over the last three weeks from 27.3 to 25.2 (it went from 25.5 to 25.2 last night alone after filling-up with high-octane gas).

Any ideas where to look and what to expect?

my brother just had the same problem a couple months ago with his 94 325i... what it might be is the guibo, or flex disk(coupling) it has a thousand names but basically it is the rubber connector that joins the driveshaft and driveline. its relatively simple to replace if thats the problem. and if it is not the guibo its could be the center bearing that supports the driveshaft halves. now that would be a bigger problem and is something that would be done in a shop. to check these two things, remove the exhaust, remove the heat sheilds and at the very back of the transmission there is a big rubber donut with six bolts, inspect the donut-esk connector and if is ripped or torn thats your problem. if its the center bearing that is broken straight back from the trans there should be a bearing bolted to the underbody of the car and it could be broken.

check those out and go from there

Took it to BMW Service today. $345 later, they "recommended" a new driveshaft. Total cost for service: $1100. Does this sound reasonable?

I had a similar issue with my '86 325. I had the Center Support Bearing replaced and all of the Staked Drive Shaft Universal Joints replaced for about $850 total.