When Tenchi catches Ryoko during her battle with Kagato in episode 6, he tells her "I still have feet". This was Tenchi's way of reassuring Ryoko that he's not dead. In Japanese folklore, ghosts are typically portrayed as legless.
Ryoko name is a common Japanese name, yet the kanji used to write it is far from being a common reading. Translated, Ryoko is "One who summons the spirits of rocks and trees". Ryoko tells Ayeka this fact during their duel in episode 4, when she summons a water elemental.
"Tenchi Muyo" is a Japanese pun. In normal usage, this kanji compound means "This side up", and is often seen on boxes and crates. (This is why the North American dubs use a "stencil" font for all the English titles.) In this series, however, it is read quite differently. "Tenchi" refers to the main character, and "Muyo" means "useless". The title could be translated into English as "Useless Tenchi", or "No Need For Tenchi".
This series is not considered canon to the other Tenchi Muyo OVAs, the Tenchi Universe and Tenchi Muyo GXP TV series, or to any of the three films.
In "No Need for Swimsuits," Ryoko lists her interests as "sleeping late, drinking early, and taking baths in the morning." This might seem typical of Ryoko, but she's actually using a line taken from folklore of the Fukushima prefecture. According to the story, the son and heir of a rich family "Shosuke-san" lost his fortune because he loved "sleeping till late morning, drinking in the morning and taking a morning bath".
The series originally ended on a cliffhanger, never explaining who Lady Tokimi was or why she wanted Washu, nor was this ever addressed in any other adaption of Tenchi Muyo. However, new OAV episodes were in production and distributed in Japan from 2003-2005. The new episodes will directly pick up where this series left off and will explain all of the dangling plot threads.
According to some sources, Tenchi series was conceived as a sequel to Bubblegum Crisis, focusing on the day to day activities of the Knight Sabers. This was quickly changed when it became a question of ownership (AIC and Artmick both claimed ownership of Bubblegum Crisis). So, they changed it to a crazy harem comedy science fiction show.
Co-creator Masaki Kajishima named some of the characters after locations in his home locale of the Okayama prefecture, Japan.
For the earlier episodes, the English voice actors had to assume pseudonyms as, at the time, the production was outside the actors' union system.
Sakuya's eyes change color noticeably over the course of the series, and range from a vivid green to a sky blue.
In the final episode, the psychic explosion from the beginning of Akira (1988) can be seen on a television screen.
For broadcast on Cartoon Network, the girls had swimsuits digitaly painted on them to either hide their nudity or to suggest that they weren't completely nude even when their bodies were covered. Also, any time an alcoholic drink was mentioned, it was dubbed over with "tea".
Katsuhito Masaki and Nobuyuki Masaki are named after AIC directors Katsuhito Akiyama, and Nobuyuki Kitajima, respectively.
When Washuu dons her nurse outfit in episode 7, her computer says "Ben Casey". This is a reference to the 60's doctor drama Ben Casey (1961).