The voyages of the Starship Enterprise are logged via stardates, and these seemingly insignificant set of numbers are meant to mark the episode's place in the series' timeline.
They sound like serious business, but how much thought and effort is put into continuity in the Star Trek series' in terms of stardates?
Well, as Chris Higgins of mental_floss discovered, the stardate system used in the original Star Trek series was "totally bogus" by design. Here's a snippet from the series bible:
Pick any combination of four numbers plus a percentage point [ed. note: tenths digit], use it as your story's stardate. For example, 1313.5 is twelve o'clock noon of one day and 1314.5 would be noon of the next day. Each percentage point is roughly equivalent to one-tenth of one day. The progression of stardates in your script should remain constant but don't worry about whether or not there is a progression from other scripts. 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.
However, the writers and directors of Star Trek: The Next Generation were given an updated system that actually worked, and with the updated system we discover that one season of the show amounts to 1,000 days:
A stardate is a five-digit number followed by a decimal point and one more digit. Example: "41254.7." The first two digits of the stardate are always "41." The 4 stands for 24th century, the 1 indicates first season. The additional three leading digits will progress unevenly during the course of the season from 000 to 999. The digit following the decimal point is generally regarded as a day counter.
Of course they still goofed here and there, but that's a way better system than "pick four random numbers and a percentage point".
Read more about Star Trek's Stardates system at mental_floss