OK, this turned into a nightmare for me and maybe my problem can be a lesson to anyone who wants to try this procedure out in the future.
I managed to get the arms straight again and put in new sliders. Everything went great. I tested the window at least 20 times and it went up and down as it should. It was working perfectly.
That was until I did the slam test! Slamming the door with the window all the way down is not a good idea if the weather strip is not back in the top of the window to give it a little support. Bare in mind that these are old cars and have weakened over time. In my case the internal guide rail broke off when slamming the door. I didn't know it until I tried to operate the window again but anyway, here it is:
As you can see, the entire rail is held on by 2 tiny flimsy spot welds that snapped off when slamming the door.
Here is a picture of the inside of the door itself.
The 2 spot welds are at the bottom end of the rail, and in actual fact I would not be surprised if they were failing anyway and the root cause of the problem to begin with.
A word to the wise...DO NOT SLAM YOUR DOOR SHUT WITH THE WINDOW ALL THE WAY DOWN AND WEATHER STRIP NOT IN PLACE!
As for me, I guess it's off to BMW to have them fix it. Oh well.