So with that being said, is it "ok" to apply to grad school with such a loose set of interests?
I think it will be much better for your application if you are focussed on something a bit more specific. It's also better for you if you know what you want - you don't want to be stuck in a field you realise doesn't interest you after a few months.
My advice would be to get a bit more experience before you go into a PhD program. Why not do a research master's degree first? That way you get an idea of what goes on and what you'd be doing, but you're only signed up for a year and you might get a chance to work in a few different labs in that time. The qualification will only strengthen you application. If you're still doing your degree try to get summer projects in the research labs at your University. I would certainly recommend getting some lab experience in order to make an informed decision about your PhD.
It just occurred to me you're probably in the US, where as far as I understand it master's courses are not very popular/available (I could be completely wrong), but a masters to get some real experience before a PhD is very common here in the UK.