First off I will state that if I want to see more of these things in fan fiction, I should stop being lazy/insecure in my writing and write the damn stories myself. If I do so well enough it may inspire others to do so. That said I am insecure in my writing and lazy, so hence this list (there is some small hope that this list itself will inspire someone to use them).
Second thing I want to say, before I get to the list, is something I have made mention to before; I really do not understand why some things become so common in fan fiction, many thing which blatantly contradict the source material, and other things actually seen in the source material, repeatedly even, do not.
1. Ranma reading.
2. Konatsu - He is an interesting character with some pretty cool techniques and I would like to see more fics with him in it.
3. Ranma attempting to be a matchmaker. Ranma tried to hook Happosai and Cologne up, he did hook up Akari and Ryoga, and he started to teach a clone of himself how to pick up guys.
4. Ghosts, Oni and miscellaneous other Kami. There are quite a few arcs that have supernatural creatures in them and they don't appear very often in fan fics.
5. Ranma being money savvy. Ranma does display knowledge on money. I mostly want to see more of this to counter all the fan fics in which Ranma borrows money from Nabiki (which Ranma never does in the manga), fics in which he gets tutored by Nabiki on how to use money (which doesn't make sense to me since he knows she would cheat him, she will recklessly use other peoples money without worrying, and will sell people out) and considering that he was on a life long trip in which he likely had to make do with very little money fairly often and probably had to deal with people trying to cheat him; it just makes more sense for him to be money savvy (he does barter with Nabiki, cons people for discounts, expressed sadness at having to spend money, expressed worry about money, has taken jobs - once explicitly for money, etc., in the manga).
6. I would like to see more fics with healing things like Ranma doing first aid or cpr (both of which he did do in the manga), physical therapy, meditation (also seen in manga both in the form of prayer and while sitting upside down), massages (again seen in the manga multiple times; once even during a battle), pressure points/shiatsu/Moxibustion for their more common healing purposes, teaching (very important to prevent causing harm), etc.
7. Ranma being sarcastic and pointing out the stupidity/hypocrisy of the people around him. Ranmas fanfiction incarnations generally are not very sarcastic whereas he is pretty sarcastic in the manga.
8. Ranma with black hair like in the manga, or black with red in it like some Japanese people really have but isn't readably noticeable unless backlite, and having different hair styles on occasion such as hanging loose or a ponytail (like Ranma had his hair pre-dragon whisker).
I am likely to add more to or revise this list at a future date.