Dinosaurs might be able to live in today's atmosphere, but a dinosaur suddenly transported into modern times might have other issues.
Plants have evolved considerably in the last 65 million years. Grasses and flowering plants really only came into being near the end of the Cretaceous period, so dinosaurs from earlier periods would have difficulty even recognizing them as food. As well, plants have evolved various toxins and other strategies to resist being eaten, which might poison a dinosaur or make it very sick. As well, dinosaurs might develop severe allergic reactions to modern plants. Herbivorous dinosaurs would, for the most part, require gigantic amounts of plant matter that they could digest. It is thought that the sauropods ate coniferous tree needles, for example, so a herd would lay entire forests to waste, and you would need a vast area for them to roam and the trees to recover.
Carnivores might have many of the same issues. The other problem for apex predators is current megafauna would only be sufficient as an appetizer or snack, rather than a full meal. Bringing back T-rex would put you on the hook for some pretty hefty bags of dino-kibble, or a large Texas cattle ranch.
Some "do it yourself" projects are underway to see if evolution can be essentially reversed in chickens to make a pseudo dinosaur, and if these efforts are successful, then Chicken-rex will be much better adapted to modern environments.
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