I have an '87 325i convertible (122K). It runs rough when it first starts up, missing and sputtering a bit. After it warms up, it runs fine.
If I start it up and drive to the gas station - 3-4 miles - it will run rough on the way. I shut it off, put gas in it (the car will sit for 5-10 minutes) and start it back up, it runs smooth.
If I don't stop for gas, and drive past the station, it's another 3-4 miles before it smooths out, so it's something under the hood that needs to get hot.
O2 Sensor(s)?