Why did Gandalf let go and fall off the cliff?

[Mister Underhill]

I haven't seen the movie since around the time of its release, but I recall the Bridge scene being one of the better played moments. McKellan did a good job of showing Gandalf's fear and humanity.

I don't think you can fault PJ too strongly for the way he played the scene (without having seen it in a while -- I really need to rent the DVD, I reckon). Anyway, the scene highlights the difficulty of adapting book to film. A straight adaptation of the text:

He staggered and fell, grasped vainly at the stone, and slid into the abyss. 'Fly, you fools! ' he cried, and was gone.

...would be hard to pull off to say the least. It's easy to imagine Gandalf's dialogue looking more likel, "Fly you fooooooooooollllsssss!!!", the last sounds trailing off as he falls -- silly. You have to give him his moment to show that he knows what's about to happen and that his last thoughts are -- very typically of Gandalf -- not sentimental, even on his own behalf.