After a troubled teen girl is caught vandalizing state property, she is ordered to spend 6 months in juvenile detention center; where she falls in love with the, married, faculty art teacher.

I infer-- because it's not stated in the logline-- that the falling in love is mutual. If that is the case, then there are all kinds of potential conflicts and complications.

And stating in the logline the explicit reason why she ended up in juvenile detention seems extraneous. Isn't all we need to know up front is that she's a JD serving time?

Intriguing start, but I agree with the others. We need to have some sort of conflict.

Decent punctuation would certainly help. We do need to know the conflict, which helps distinguish what is in the logline from backstory and the actual events of what you're proposing to write.