How did Ozzy and Strut ever manage to get away alive and unhurt from the volcano? The last we see of them is them falling / jumping into a canyon of undetermined depth with lava pouring into that canyon from above.
Oh, I don’t think the writers and artists were as careless here as they are often made out to be. I think one picture answers the question of their survival quite nicely. You see, I disagree that the depth was undetermined, and escaping the lava flowing down is merely a matter of gravity of saving the day. The image I am referring to is this:

As you can see, the depth is shown rather clearly. Furthermore, the lava is flowing down from the right side of the log. Looking at the ground, you can see that it is at a sharp decline, and the downward slope is also going right. Therefore, it makes sense that when the log collapsed, they avoided the lava entirely, because it was flowing downward, not filling up an area, and the flow was far enough away from the log’s dropping point. Now, just before the log collapses, we see that it is starting to flow below the log, but it starts so soon before the log breaks, and the flow is so slow, that it still makes sense for them to hit the bottom long before the lava reached the point where they landed. The drop really isn’t that large for a dinosaur, especially an adult, to fall into. Several adults fell from a much larger cliff in III and had no apparent injuries at all. So surviving the drop itself makes sense. Avoiding burns makes sense. They clearly just ran up the incline to get away from the lava.
Another not quite so spectacular but nevertheless noteworthy off screen matter would be whatever Cera, Ducky, Petrie, and Spike were doing during the final part of the movie. It is arguably simply poor script writing that from the moment Ducky announced the likelihood of "big trouble" to the farewell to Chomper we didn't see anything of them, presumably because they wanted to focus on Littlefoot and Chomper only in that scene. The matter of the difficult relationship between everyone but Littlefoot and Chomper was therefore kind of abandoned as an element of the plot. But what exactly WERE Cera, Ducky, Petrie and Spike doing during that time?
The kids knew at this point that they were in trouble after what happened, so they probably did not want to get on the bad side of their families any further. When Littlefoot ran off, Cera explained why they stayed. “Your grandpa said to stay here!” The kids don’t ALWAYS disobey, as we can see, at least, not at first. I’d wager they did as they were told for a while, then decided in the end that they really should help Littlefoot after all. Remember VI? Littlefoot decides to fix things and they stick around, then they suddenly realize how big of a deal it was what he had in mind, so they went after him. “You came for me!” “Don’t we always?” So as far as I can tell, they knew the thin ice they were on so obeyed at first, but their concern for Littlefoot won over and they went after him. It is possible that they even went after him fairly quickly after he took off, and the reason their meeting took so long was simply that they could not find Littlefoot very quickly. I can see one of them shouting, “Hey, I finally found Littlefoot! He’s up on that ledge with Chomper. Let’s go see him off.”
Obviously the did ignore the grownups order to stay where they were and they even managed to get to the gap in the wall before the grownups did (who by the laws of time and likelihood probably ought to have been there even before the eggeaters and Littlefoot).
The Great Valley is large. The adults did not even notice the hole until the kids said so. Furthermore, after the grownups learned of it, they never asked the kids where it was, so they clearly went off searching for this hole on their own with no guidance, so it would make sense for those who knew where they were going to get there before those walking aimlessly.