More than an hour was cut from the film to make the 3:20 run time for the theater.
How much gets added back in for the extended DVD version remains to be seen.
What is not explained about Denethor (at least in the theater release) is the fact that one of the palantir (seeing stones) is in his keeping... and he has been using it for quite some time... Sauron has corrupted Denethor's mind with images of the fall of Gondor.. Denethor has given up all hope. Boromir's death seals Gondor's fate as far as Denethor is concerned.... the final nail in the coffin, so to speak.
That is why he behaves as he does...
I think the scene of Denethor running (burning) from his pyre and jumping off the cliff was an unnecessary twist to the story (Shadowfax should not have kicked him back onto the pyre either, he should have burned willingly). Besides, he would have suffocated, fallen and burned long before reaching the cliff anyway... he was no super-human.
Apart from Denethor's cheesy-movie-death scene, I think the third film was very well done and it stuck more true to the original story than the first two films did.
Can't wait for the extended version

:)
Edit:
I agree that such a long ending after the film's climax is tiresome (for a movie... better to read the book)... but the story has so many characters and different plots within it that all need to be resolved. They could easily have spent another hour dealing with "Sharkey" and the scouring of the Shire and the hobbits becoming the sheriffs of the Shire etc. ... but how would a movie-going crowd accept it? Probably not well at all.