Is it okay to wear shoes half a size too big?

It depends on your goals, the purpose of the shoes, and on your feet. If the shoes are meant to be more of a performance fit, then they should not be too big or loose. If they are meant to be a comfort fit, or shoes for warming up and for easier routes, then they can be slightly bigger if you feel it's necessary.

All of my climbing shoes are half a size bigger than my street shoe size, and this is a performance fit for me. I have flat and wide feet, and have found that going up half a size is the perfect fit for me. It's not loose, but it also isn't painful.

Also consider that if you are buying leather shoes, they will most likely stretch by half a size up to 2 sizes, so if they are half a size bigger when you buy them, they may very soon end up being over a size bigger, or more. So the type of shoe you are wearing also matters when answering this question.