Let me start with the obvious ones that have ben most noticable in my extensive shopping and limited user experience.
Moving from a fixed lens digicam (say a high end one like the Minolta A2 that Michael Reichmann seems to like a lot) to an interchangeable lens DSLR, here are some plusses and minusses.
+ I greatly prefer the optical through the lens viewfinders for the common reasons of the sharper image and better performance in low light (for now, but "video viewfinders" are improving)
+ better AF performance and shutter lag in general, far better in my experience, partly due to the ability to use phase detection rather than contrast detection AF
+ a far greater variety of lenses, including some likely to be of far higher quality than any on a fixed lens digicam
+ higher usable shutter speeds (at a cost in depth of field), ultimately because the SLR lenses have physically bigger apertures and so can gather more light from a subject.
+ more capability to achieve very shallow depth of field and so blur out distracting backgrounds, or even foreground elements that pass directly in front of the main subject (due again to the physically far larger aperture diameters).
- greater size, weight and cost (I said I was going to state the obvious)
- no live video viewfinder, either back panel LCD or EVF, so no live histogram, or flashing highlights, or zooming for manual focus, or "exposure level preview", or ...
- no video recording ability
- sensor dust; but see below
Non-differences and less important ones.
= DSLRs do not inherently suffer from having less depth of field; you can roughly match the high DOF of a compact digicam by stopping down a DSLR suitably and then adjusting the "ISO" speed up to get a comparable shutter speed, and still end up with comparable noise levels, at least with many DSLR's.
= Interval photography: at least some DSLR's support interval photography. For example, the E-1 offers this, but only through tethered operation and with the Studio software, which costs extra.
= The mirror slap on my Olympus E-1 is so quiet that I doubt it will have much affect on image sharpness, though I have not tested that formally. That is an advantage of smaller format DSLR's with proportionately smaller mirrors compared to larger formats; the momentum of the mirror reduces with the cube of format's linear size. However, I believe that many APS format DSLR's still use full 35mm format mirrrors, so do not yet have this advantage.
= As a new E-1 user, I have seen no sensor dust yet and am for now optimistic that the "sensor cleaning" mechanism will minimise this much discussed annoyance of interchangeable lens DSLR's, but mostly on the basis of reports from other users.