The question of this thread was also brought up in a fairly large GOF-MSN chat yesterday.
One thing to note is that slapstick moments, which contribute a lot to the "light" rather than "dark" atmosphere of a movie, are by no means an invention of the sequels and on the other hand sharpteeth didn't turn harmless right after the first movie either.
Still there is a distinct difference between the general mood of the first movie and the sequels which I think is based on a number of points.
Most important, I think, is a kind of sense of a "changing world" and the passing away of dinosaurs as a whole in the original movie. While this idea is certainly not found in the sequels.
In the original movie we have the impression of a "dying" world with the Great Valley being the very last save heaven. There are unproven but not incredible rumors that the original concept of LBT meant Littlefoot and the others to die and find the Great Valley as a kind of dinosaur heaven rather than a real place (a place to see with your eyes rather than with your heart only). Now I'm just guessing, but apart from that being a rather tough story the similarity to the (more lighthearted) "All dogs go to heaven" may have played a role in the decision to choose a different way for LBT. If that original idea really existed and if it had been realized there would have never been any sequel at all.
Anyway, the sequels' image of the world of LBT is a very different one. The first two sequels (LBT 2 and 3) still at least don't contradict the image of the Great Valley being the last green heaven. The Mysterious Beyond is depicted as VERY hostile there (dinosaur skeletons everywhere) and we never hear of any other places like the Great Valley. LBT 4 was the first to break with that tradition by including the Migrating Herd. The Great Valley is no longer the only place where dinosaurs could live. Nevertheless a some of the elements of the original movie are maintained, but while the changes in the original movie were clearly changes to result in the doom of dinosaurs LBT 4 gives a very different outlook on these changes. The nice little quote: "The land is changing. Maybe we will all live together some day." Certainly gives a very optimistic interpretation of changes that does not seem to fit at all to the changes mentioned in LBT 4 (the land of mists becoming uninhabitable for Ali's herd).
LBT does show a struggle for the life of the characters with the strenuous journey of the Valley inhabitants. This journey however was only a short scene and we never actually saw somebody dying (we only got to see the skeleton of a duckbill who didn't belong to the Great Valley herd). Nevertheless I find Pokeplayer's recent theory that it may have been during this journey that Cera's mum and her siblings died quite interesting. In the end of the movie however we get a glimpse at another "Great Valley" for the first time in the series.
LBT 6 finally kills of everything that may have been left about the Great Valley's mythological status "This place is nice, but there are others just as nice out there somewhere."
The status of the Great Valley as just one among many in a basically healthy world is in my opinion an important factor to change the general mood of the movie. There are still "dark" elements in some later sequels (Pterano incident in LBT 7, a "good" sharptooth in LBT 9) but none of them comes even near to the dark mood of the original movie.
Personally I don't think lighthearted elements in general are to be condemned, so I guess my vote too would go for a mix of dark- and light-hearted elements. I suppose that such a mix would look similar to the early sequels which I prefer over the late ones.