It is your responsibility to pay attention to the signs, however, it has to be in a conspicuous location and I believe it has to be one of the legal anti-CCW signs, not just something they made it Microsoft Paint.
If they did their part, and you missed or ignore it, then you could be charged with criminal trespassing. If they don't have a sign, but say they happen to notice that you're carrying, and they ask you to leave, and you don't, then it's criminal trespassing.
As for someone accidentally seeing your gun; that's their problem. So long as you aren't pulling the thing out and waving it around, you're fine. As was said by someone else; Ohio is an open carry state as well, so even if it is showing, you're OK.