Parts of the missing footage are known. Don Bluth wrote in his toontalk magazine that nineteen fully colored Rex scenes were cut from the movie. Between 8 and 9 minutes were cut. Not all scenes are scary T-Rex scenes though. The original story was that Littlefoot found the Great Valley shortly after his quarrel with Cera, but rather than entering it he turned back to get the other who he knew were on the wrong way. There are some images which prove this scene was actually created. There are two pictures showing Littlefoot at the waterfall above the Great Valley. In one of which he turns back. Neither of these pictures has been in the movie. As for scary sharptooth scenes, one cut scene was even part of the trailer, but not of the movie. You can see Ducky in shallow water pulling faces at somebody who is almost certain to be sharptooth, for suddenly you see a shadow and Ducky looks quite terrified. The scene was most likely cut from the final fight of the sharptooth. Some LBT books published along with the movie include scene which I think may well have been part of the original concept. An example is one book telling that sharptooth lost an eye when he pursued Littlefoot and Cera through the thorny shrub. There is a scene in the movie in which a thorny twig snaps into his face and you can several times see that something doesn't seem to be quite alright with one of sharptooth's eyes. Maybe scenes about this were cut. As Don Bluth had problems to consider Sharptooth (who only obeyed the laws of nature) a villain, he may have attempted to give him some evil quality by pursuing Littlefoot because of revengefulnes.
There was a page (I have the text saved somewhere) claiming in a trustworthy manner that Don Bluth meant the movie to be 35 minutes longer than it is now. He was overruled, so those 35 minutes were never produced. Some LBT books published in 1988 give scenes which may have never been produced (though I can neither prove that they were nor that they weren't) but which may have been part of this 35 minutes concept. There is one scene in which Littlefoot and the others reach an oasis whose water is guarded by bigmouthes while the trees are guarded by domeheads. Neither of them shares with the others and neither is willing to share with the kids (except for the bigmouthes allowing their kinfold, Ducky, to drink). The way it is described in that book that scene seems to have made quite an impression on Cera and helped to cure some of her racism.
Finally there is a scene which was not in the movie, though a picture of it was used in cinema displays in 1988. The scene must take place right after Spike's birth. You can see Ducky, Littlefoot, and Petrie gathered around sleeping Spike. Ducky apparently tries to make him come along luring him with a stick from which some red berries dangle. You can see that very stick in the movie, in the scene after Spike's birth. Another picture of that scene was published on the official land before time page and you could see Spike sleeping while Ducky standing in front of him turned her head to Littlefoot (right behind her), apparently talking to him. Some of the 1988 books suggest that Cera argued against the plan to adopt Spike.