If the spots look eaten through, is it possible they have leaf miner?
This plant does best in full sun according to the Missouri Botanical Garden. Here's their page for 'Blue Moon'.
http://www.missouribotanicalga...
Unless the plant has hairy leaves it's not likely to be burnt from watering even if it was outdoors and watered in mid-day sun, which you say it wasn't. I assume also that being indoors you aren't getting the leaves wet when you water? Watering at night is best avoided because it promotes fungal diseases but again I'm assuming you don't get the leaves wet?
If anyone is interested here's an article about research that showed plant leaves that are not hairy do not get damaged by watering in the sun:
http://www.americanscientist.o...
