I already PM'd The BOSS with further explanation (and he has successfully replaced the lower window moulding as well! Good going--another cleaner e39 on the road!).
But I should add an addendum to this write-up based on a few additional emails I've received. I should have expounded more on removing the main wiper arm. Once you remove the cover of the driver's side arm, remove the top bold. Underneath that is a gold "pressure" bolt that holds the mechanics to the whole shebang together. I don't know of any specialized tool that can assist in removing this bolt. You need a set of heavy duty grips, like large quality pliers, and a rubber mallet. Careful using a metal hammer, but that can be used as well. The bolt is VERY sturdy and can take a lot of punishment. Basically, you need to beat the crap out of the bolt (but carefully, if that makes sense) to loosen it up. Alternate between whacking it with the mallet and jiggling with the pliers. Anti-seize solvent may help. Have patience--it WILL loosen and come off.
Also, a tricky part is replacing the wiper arms in a proper "rest" position after you've installed the new cover. It's a little tricky, and may take between one and three tries to get it right. Put the wipers in the "rest" position and reinstall the wiper bolt including the pressure bolt, but not TOO tight since it is likely you will need to remove and reinstall again. Don't replace the plastic covering quite yet. Once in place, run the wipers and turn off. The wipers will likely rest a bit too high. Remove the bolts, tighten up and try again. After two or three times, they will be back in position. Have some patience and you'll be happy. Enjoy your nicer looking window mouldings!
'07 335xi 6-spd 4dr, Montego blue
'98 540i 6-spd Sport, Jet Black II
'92 325i 5-spd 4dr, burgundy