I picked up 2 Anthurium after the holidays at a discounted price. I decided it would be best to acclimate them to their new surroundings before doing anything to them. After about 5 days I gave them a little drink of distilled water being careful not to let the plants stand in water for any length of time. Then I placed them back in the bathroom which has large east facing windows which provide good light for several hours. I don't let the leaves touch the glass of the windows or the wall. There are no drafts and the temperature stays around 70 degree with fair humidity. I noticed the leaves had started to turn brown on the edges with tons of brown spots throughout its length. The tiny brown spots are just on the surface and don't go through to the back of the leaf. Even under close inspection, there are no bugs that I can see. I believe the problem may be systemic but I don't know what. Would cause this to happen. I've only had the plants for about two weeks so I haven't done anything beyond watering them. Any suggestions?

E.