Well, I think we can safely say that Lily can be a bit blind to other people's flaws (ie, Peter Pettigrew) and she put up with Snape for a long time, even though she said in the DH memories she didn't like the people he was hanging around with and the things they were doing.I also agree with the Lily-Sue thing. While we're on the topic, what do you think could be some serious flaws that Lily could have to make her seem more...human? I've tried to write her before, and found it extremely hard. So far she only really has two minor flaws: her inability at Quidditch and her temper, and having a temper is used so often it's a total cliche. Any ideas?
She also can hold a grudge for a VERY long time. After Snape called her a Mudblood, she completely didn't want anything to do with him. You can glean from that information that she is stubborn. You could also say she might be a little ashamed about her parents, as a famous Hermione qoute is "Mudblood and proud" and we never hear Lily say anything like that. While Hermione is comfortable and doesn't see it as an insult, it is enough to make Lily fall out with someone who she has known since birth.
That would actually be a good angle to use. Making her be a bit insecure about herself would break away from the Lily-Sue thing. She could desperately be trying to proove herself as a witch and be a bit closed off from people who have different blood status, in case they make fun of her. It would take her a long time to truly let someone in and after that, she would definately become fiercly loyal; after all she died for Harry and loved Petunia even when she was calling her names.
You've got to remember the way she is represented in the books is purely from Harry's view. Harry owes her a life debt, so he's hardly going to sit there and talk bad about her. In Harry's eyes, his mother was perfect and he didn't go on the look out for her flaws.
I personally don't think she would be highly strung or bossy. I think she would only truly get angry when someone she loved was threatened, as shown in OOTP Pensieve scene. She wouldn't really have the confidence to be bossy at the beginning of her Hogwarts days, because she was going into the unknown. As she got older she would probably get more comfortable and therefore, feel more at home keeping order around Hogwarts, but I definately don't think she'd be anything like Hermione or Ginny, because they had completely different childhoods.
Hermione was probably pampered as a child, and Ginny was the youngest of seven, while Lily had one sister. I think another interesting angle to use when writing Lily is her relationship with Petunia, and how she is torn between her sister and her magic.
Hope this helps!