What is her relationship with her parents? Are they too close so that they have control over her life? Or does she hate them and constantly complain about them. Some girls might have issues with their parents and not be crazy, but all girls that are crazy, have issues with their parents.
An obvious sign of crazy is the medications she is taking. Next time you are at her place, take a quick look in the medicine cabinet when you take a piss. Any medications related to mood regulation are a sign to pretend you have to get up early in the morning and leave.
Yes, political and environmental science is not a sign of craziness. But think of the right-wing, tea-bagging, Republicans out there? Would you consider them crazy or totally sane? If she truly doesn't believe in global warming, you have your answer.
Talks About Her Ex:
If she is talking about her ex on a first or second date excessively, make sure to accept her offer to split the bill and get out. She doesn't understand appropriate dating conversation and is obviously still hung up on him.
Her Illness List:
Yes, people have physical and mental ailments. People suffer from depression and anxiety. And at some point in a relationship, it is worthwhile to have these conversations, but not on the first date. If she informs someone she just met that she is taking depression medication, she's searching for sympathy and wants you to be the guy who makes her not depressed. And if she is complaining about her bad back on a first date, imagine listening to her on a road trip or airline flight.
Abuse, Assault, Etc.
From personal experience, 98% of all women have been raped, abused, or molested. Most of the time they wait till the second date to tell me how their ex-boyfriend beat them. But sometimes, they will tell me about the time they were date-raped on the first date. Yes, terrible thing to have to happen, but would a sane person tell a complete stranger about the uncle who molested them as a child on a first date.
Pets should be capped at two. Always! If she has more than two, ditch her.
If she is more comfortable having a conversation with you in text messaging over face-to-face, and in an e-mail or regular conversation uses acronyms excessively, ditch her. She has no personality.