Composition: get closer, most holiday snaps are too far away from the subject; wide-angle shots are key - and the subject has to be prominent in the frame. The famous photojournalist Frank Capa said it best - "If your pictures aren't good enough, you're not close enough."
Lighting: open up the shades, turn up the lights. Sacrifice a little bit of the ambiance; your camera operates best with as much illumination as possible, both for focusing and image quality.
Video: it's available now in many digital still cameras - but the rules are the same as still photography - strong light and a steady hand and avoid zoom transitions - the latter is a technique used in many award-winning films.
Audio: the other half to a successful movie - if your camera supports it, connect an external microphone to get the best sound possible. Otherwise, get closer.
Background: Don't forget to get some good frames of the main course (before it's consumed) and the decorations. Ditto for when the Tree and presents come out.
Timing: catch the candid moments, but avoid taking shots of people eating - follow the rule of photographing royalty - nothing in or near their mouths.
Posing: group shots can be deliberate but should be dynamic. If you must have posed formal shots, do so before anyone has had anything to eat or drink so as to keep appearances as neat as possible.
Flash: in some cases you must use it. That's okay. If you have an external flash for your camera, look for places to bounce your flash off of - white walls and ceilings are best so as to simulate natural lighting color. On cameras with built-in flash, try cutting up an old ping-pong ball and stick on top of the flash - presto - instant diffuser for softer lighting. For video, you may need an auxiliary white light to get good footage.
Keep Shooting: you've got extra cards and batteries right? (if not, this is a BIG HINT) Keep shooting so as to get the maximum number of opportunities.
Pay now or pay later: while you're digesting the excellent meal, take the time to sort through your frames and clips using the preview function and delete the non-keepers. Either way, be prepared to get some serious post-processing time on the computer to enhance the really important shots and splice the vidclips into a cohesive narrative. But every minute you spend QA'ing the "take" in the field translates to less time spent behind the keyboard sorting and culling.
Above all, have fun! Happy and Safe Clicking!