I'm not really picky about grammar. If it's so bad that I can't understand the story, then we have a problem, but otherwise, just try to use corret sentence structure and keep your verb tenses the same. Writing a fanfic isn't English class or anything, so just do your best.

Punctuation. I'll admit that I suck with punctuation. I never know whether to put a colon, comma, period, semi-colon, etc etc...so who cares! I have come across some fanfics that for some inexplicable reason have periods after every second word though...

Whatever you do, spell the character's name correctly. I hate reading a fanfic and finding a name misspelled! Poor Doctor Fraiser seems to be a common victim of this one. I've seen her last name spelled as Frasier, Fraizer, Fraser and Fraisier.