Increased oxygen density is certainly a leading theory for insect giantism in certain periods of the Palaeozoic, but the principal behind it wouldn't apply to vertebrates (we discussed it a few pages ago).
I suppose you could speculate that higher oxygen intake could have given dinosaurs more energy, and that they might have used the energy to carry greater bulk around with them, but aside from the concern over whether that would be physically plausible, the oxygen content during the Mesozoic is actually uncertain. Some estimates put it lower than today's.
My personal theory is that dinosaur giantism stems from the need for the herbivores to develop giant stomachs. This gave them greater capacity and efficiency in fermenting plant matter. There are two reasons why this was so important. One, the Mesozoic was dominated by extremely tough plant material that most of today's animals struggle to digest, if they can at all - conifers, cycads, ginkgos, horsetails, ferns. Two, many dinosaurs lacked cheeks or grinding dental batteries, so their stomachs (and swallowed gizzard stones) would do a lot of the work that mammalian grazers' mouths perform.
A giant stomach needs giant legs to carry it, giant muscles to propel that bulk away from predators or onto a mate, a giant mouth to shovel down food quickly enough, a giant neck to reach the ground, and a giant tail to balance the neck.
And of course, predators evolve to match their herbivorous prey, which is why the allosauroids appeared when sauropods started to dominate.
There are other theories, and probably more than one of them are true.
The herbivores and their predators could have been locked in an evolutionary arms race, each undergoing natural selection for increased size as a tool for defence / predation. I'm sure this must have been going on, but doesn't explain the situation in itself - why aren't mammals prone to giantism for the same reason?
Temperatures dropped during the late Jurassic, concurrent with the appearance of colossal sauropods and allosaurs; it's possible (just) that this may be a thermoregulatory development. Larger animals retain body heat more easily, and as we've never found evidence of protofeathers in either group, temperature may have been very important for them. (Personally, I suspect it's only a matter of time until we find feathery baby sauropods and non-coelurosaurian theropods.)
Another theory is that dinosaur populations could survive with few adults compared with mammals, because they didn't need to put as much effort into raising their young. With less adults, there could have been more food to go around, allowing them to sustain larger sizes. Maybe.
Sexual selection has also been proposed... larger dinosaurs won intraspecific contests, or were more attractive to mates.
There's also an old theory that animal groups will simply tend towards giantism if they have the physical tools and requirements for it. But it was proposed by the bloke who put Elasmosaurus' head on the end of its tail, so might be best not to put much stock in that one.
There are other theories I can't think of from the top of my head, and there would certainly have been other factors involved.