Is it safe to eat food imported from China to the US?

There’s a pan-Asian grocery store that opened fairly close to my home (in Ohio) recently. It has food from all over Asia, but seems to have a heavy focus on Chinese food (much of it imported from China.)

On one hand, I’m curious about trying it (and have no reservations about the obviously fresh food.) On the other hand, I’ve also heard a lot of horror stories about Chinese companies putting things that should not be in food in their food. (I don’t think the store would stock questionable food deliberately, but they might unknowingly.) I’m not sure how much truth there is to these stories– I don’t doubt they happened, but as far as I know it could be xenophobes making mountains out of molehills.