Mihoshi is a... *ahem* unique individual. She is a member of galaxy police and a good detective, but she is outwardly quite dumb. Her grandfather is the martial of the galaxy police and maybe the only reason that she is a first class detective. In any case Mihoshi isn't all that bad at her job, just a little rusty.
In OAV #5, Mihoshi, Tenchi, and Ayeka travel in Ryo-ohki to fight Kagato and Soja. The three didn't know how to correctly fly Ryo-ohki (because it is Ryoko's ship) and were losing against Kagato. Mihoshi found the crystal that "looked different" and thought it might help them. When that didn't work Mihoshi took some saki and gave some to the computer unit and herself. Even though this might have seemed like a stupid thing to do, Ryo-ohki's random movements (due to being drunk) effectivly dodged Kagato's attacks! Not something anyone planed on, especialy Kagato.

Over all Mihoshi is a good detecitve and even though she isn't sharp as a needle she does help the Tenchi cast get through those would-be-boring conversations with a little bit of humor and stupidity.
Mihoshi
This discription was barrowed from John's Tenchi Page
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