OK, I've got two questions about all this.
1) If the umpire signals safe, but runner did not touch home, can the defense still tag him out? Would I, as a coach not have reason to complain that the umpire signaled safe, so the assumption was that the runner was safe, therefore made no attempt to go back and tag home? Hope that makes sense.
2) I would assume that similar to an appeal play on a tag up, once the next pitch is made without appeal, the play would stand and no appeal can be made. Based on that assumption, no tag, no touch of home plate, no appeal before next pitch - does the run score? If the runner never touched home, does it still count, or does just crossing the plate area constitute scoring? Probably similar to a runner missing a base, but no appeal - no out. Just never thought about it in terms of this happening at home and counting the run.