There is 6 periods "That's if you don't include the Holocene Era of Made-Up Dinos" but Six in total that build up the Mesozoic Era. (Late Triassic, Early Jurassic, Mid Jurassic, Late Jurassic, Early Cretaceous and Late Cretaceous... the latter 3 have a long list of dinos but the first three are lacking. We only have 1 Triassic dino, 1 Early Jurassic, 2 Mid Jurassic dinos.
Largely this is probably because certain types of dinos didn't exist due to the evolution of species. I mean really only variations of Herrerasaurus and Sauropods existed from a Dino Perspective until we get to around the Late Jurassic Era.
To remedy this I posted on I think the wish list a Big Dino Expansion pack idea that fills the void with a number of dinos that visually and period specific would fix this problem.