Are things ever dialect checked? I'm wondering if things (in general) are ever dialect checked?

哈尔滨啤酒 has a commercial where they go around singing the name 哈啤 over and over again but it sounds a lot like SB in Southwestern Mandarin. (They really should have checked that.)

I'm wondering if these public things (billboards, commercials, posters, etc.) are ever checked to make sure it doesn't have any dialectical problems?
No. Once your sentence exceeds seven words, it is guaranteed that you will offend a man in the street or a women on the roof. So we just give it up.

Like the homophones in the same dialect aren't enough to deal with...

But if you are to do business in Sichuan (or anywhere actually) it's your own lookout.