Exaggerated: Robert Ainsworth, Esq. lives in Victorian England and hunts flying and fire-breathing dinosaurs for food, fun and profit.
Downplayed: A Tyrannosaurus is shown fighting a Styracosaurus (they never coexisted, but they aren't far off temporally).
The dinosaurs or Ogg have been temporallymisplaced, or a tiny pocket of dinosaurs has survived much later than their fellows.
In the show, the K-T extinction was less harsh, and allowed some groups of dinosaurs to survive in isolated pockets, away from the competition of the mammals, who had grown to much greater sizes than they were used to, until mammals migrated to these isolated pockets.
The author is a Young-Earth-Creationist, and believes that dinosaurs and early man actually did coexist.
Dinosaurs do not appear in times and/or places where they should.
Dinosaurs remain in their own time period, but everything from the distant future is barging in.