Dudley Do-Right and Nell Fenwick's relative ages, the amount of time they have known each other, and the backstories of nearly every main character, vary in almost every installment.
Snidely Whiplash's henchman Homer has a completely different appearance nearly every time he appears.
"In one episode they say this, but then in another episode they say that, and in yet another episode they say the other." As this is an animated comedy series, the emphasis is clearly on laughs rather than complete verisimilitude. Efforts are certainly made to create a vaguely consistent setting in which somewhat consistent characters live and work, but it is not necessary for all the episodes to be consistent with each other. Most contradictions between episodes should only be listed here if they are interesting to a significant number of people.
Some installments open with statements of which year the story takes place (e.g., 1903, 1905, etc.), but are full of technological artifacts which don't suit those dates.