No continuity? I think TOS season one has at least as much continuity as real life. How much continuity are you seeking? Endless references to previous episodes? Lots of multi-episode plot arcs?
Without reading the rest of the comments yet... Yes, it sounds like the OP is looking for story arcs and season arcs. These concepts weren't around in the 1960s during TOS. In fact, I can't remember such story telling methods prior to X-Files and Babylon-5. Well, that is, outside of Soap Operas.