Is it safe to reheat old water in an electric kettle?
Maybe I'm wrong, but there is no safety risk at all when boiling old water. There is however something like taste. The reason the old water is discarded is because, after boiling, it lacks oxygen and will taste stale. This is also the reason why coffee is made with 95ºC hot water, or why Moroccan tea is poured from above (to oxygenate)...

So, as long as you boil it before drinking it should be safe.