I've talked to Gareth from over at PlanetAVP in the past about AVP, and he told me that he has a source that worked on the film, apparently they told him that there were quite a few scenes and/or shots (which weren't even mentioned on the 2disc dvd) that did not make the final cut due to the fact the Visual Effects teams were not given enough time to complete the work. Actually I believe many of these shots/scenes can be found in "shooting script" that's available online.
Beyond the aforementioned missing scenes, here's some other tidbits I know about....
-There was a short fight scene between Scar and Grid filmed, it occurs in the Ice Grotto(sp?) just before Scar & Lex jump onto the emergency sled. From what I was told it was almost exactly like the beginning of the Celtic/Grid fight, Scar and Grid striking at each other while rolling around on the ground, with Scar taking out a shuriken and slicing Grid across the side of his dome then kicking him against a rock.
-Several shots in the Celtic vs. Grid scene were deleted, unfortunately I didn't get a description of what they were, although when you watch the scene the edits are quite noticeable.
-In the sequence were Scar attacks the team in the Pyramid, there was a scene cut were Scar throws a shuriken which nearly decapitates Sebastian, Lex and Stafford.
-A couple of shots in the scene were the Pred slaughter the team at the Whaling Station were cut. In the final film, we see one of Stafford's men standing outside for no apparent reason, well originally there was a shot were he catches a glimpse of the 3 Preds walking torwards the camp in the middle of the snowstorm. Furthermore, when that said character is killed, all we see in the final film is the camera in Pred POV zoom torwards his face followed by a metallic slashing sound effect, there was a shot cut of a closeup on a cloaked 'Chopper' swiping one of his giant side-blades down into camera.
-In the Flashback sequence, the massive pull-back was trimmed slightly, and just before the Pred's Wristbomb explodes a couple shots of Aliens being diced-up were cut, aswell as a shot of a Pred impaled through the throat by an Alien tail.