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's sword, makes the famous lightsaber sound from the Star Wars films.
"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".
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".