Rumor has it Mihoshi never undoes her ponytail, because if she did, she's lose her memory.
Mihoshi's robot assistant, Yukinojo, is a special model that's learned to understand its owner's rather confused command style. Other patrol ships have robot assistants but only Yukinojo talks the way he does. It isn't difficult to understand why.
Mihoshi's patrol ship changes shape between OVA Ep. 4 and 7 because it is a special self-evolving model. How did Mihoshi get such an advanced craft? Her grandfather is the head of the Galaxy Police.