Consequences of reversed polarity

It's unlikely to cause any major problems with electrical devices, but could be a safety concern if something else breaks. As you surmised, if you have a neutral-ground fault simultaneously with an open ground, you could end up with a hot skin condition. If you have some appliance or other electrical device with a polarized plug, the lines will be reversed; in the case of a table lamp, say, the threaded part the socket will be hot (and unswitched), while the button in the bottom will be neutral, rather than the other way around.

It's certainly something worth being corrected, but not really something worth lying awake all night worrying about.