Personally, for me the worst trope, or I suppose 'mistake' is when an LGBT character is identified solely by their sexuality or gender identity. They don't have any other purpose than to be that one gay, lesbian, or trans person: beyond that they are flat and without personality whatsoever.
It's why I like to include gay and non-heteronormative characters without ever telling people about it. Their sexuality/preferences come through as their character develops, so the character isn't developed for the sexuality.
And abusive/arranged marriages are quite the pet peeve of mine. It's not romantic, no matter how much you romanticise it.