There are three numbers to consider when deciding on an order in which to view episodes:
- Episode Number - This is traditionally recognized as the order in which to place the episodes and they generally correspond to the order of the dates on which they aired. This is the order in which most people might sit down and watch them, but they do not correspond evenly to their given stardates, nor do they even correspond to the order in which they were produced. The biggest discrepancy in episode numbers, however, is the fact that the pilot episode, "Where No Man Has Gone Before", was the third episode to be aired, even though there are clear production differences.
- Stardate - One might think that the stardate flows in order from episode to episode, but such is not the case. The stardate was originally invented to hide the actual date from the viewer so that we could imagine it to be as far in the future as was logical. Writers of the episodes were encouraged to come up with a random assortment of four numbers and a decimal for their stardates because "Stardates are a mathematical formula which varies depending on location in the galaxy, velocity of travel, and other factors, can vary widely from episode to episode." [sic] Therefore, stardates would never and will never correspond to any actual dates, episode numbers or production numbers because the algorithm is so complex that not even its creator knew what it was.
- Production Number - This is the order in which the production crew actually put the episodes together. Now, because The Original Series is so episodic (as opposed to other spin-offs such as Enterprise and Deep Space Nine which can be largely serial) not a lot of emphasis was placed on the order in which episodes were made as it corresponds to the date on which it was planned to air. As such, episodes may have been aired "out of order", but it didn't really matter because an entire story including plot and subplots was told and wrapped up in the same hour. It's not uncommon, really, to produce episodes of any series in the order that best suits the efficiency of production rather than the eventual timeline. There are, however several minor continuity issues that can be seen from episode to episode that give the idea of one story being before or after another; things like uniform style, acting techniques, cinematic quality, etc. Specifically, these issues are clearest in the pilot episode which was aired third.