Excellent breakdown Alexander!
In my experience, I've found the white balance adjustments to be the single greatest assets in my point-and-shoot experiences. Sure, most of this can be fixed in photoshop, but you want a good pic going in. Photoshop is not there to perform miracles. It can make a good pic outstanding, but it can't make a piece of turd anything other than a good turd. Having a digi camera that will allow such adjustments is very beneficial.
I'll probably get yelled at here, but I love the scene modes available on some dig cams (notably Olympus). They don't always work out quite right, but when they do you can get some really cool shots. The main benefit, in my experience, has been time. With analog SLRs, you can dial to different setting pretty quickly (on the fly). With the digital cams I've used, you have to dig through menus to get to the most useful settings, such as those described by Alexander above. This can ruin those "in the moment", or spontaneous, shots.
As a ageneral rule, if I'm at an event that starts in the day and ends in the night, I will typically use auto settings during the day and around dusk I will switch to a longer exposure and turn on the auto flash. Simply turning off the flash and setting the camera on a table or other flat, solid surface (with timer mode) has resulted in some really great group/scenery pictures.
Here's one I took recently of downtown Monterrey, Mexico at night with a long exposure. It's not a great picture, but it illustrates the point. The colors are very warm. Notice that blur is still introduced (likely from the table or low vibrations on the ground nearby [ie my feet]).
