First, check for red spider mite infestation, which sometimes causes these yellow spots - they are quite difficult to see. Spray with an appropriate pesticide spray if you find them. Second, these plants are said to be sensitive to fluoride in water, so if your tapwater is fluoridated and you've been using that, this might cause those brown tips, though usually the brown tips have a yellow band on the 'live' end so to speak.
The other possible cause of the yellow spots is poor drainage - do you leave the plant standing in any outer container which collects water? If so, ensure you empty the container 30 minutes after watering. Water only when the surface of the compost is slightly dry to the touch, but not so dry it's shrunken from the sides of the pot, and water thoroughly. Despite not liking sitting in water, these plants don't like to dry out and do like high humidity in the air - keep away from direct heat sources, and add a pebble tray if you think it's necessary. (Pebble tray - an outer tray larger than the pot, filled with pebbles, that you keep half full of water, so the bottom of the pot is on the pebbles but above the water - the water evaporates and keeps the air round the plant more humid). Keep the plant in an even temperature as far as possible, never below 65 deg F, and, as you've already done, out of direct sunlight.
Lastly, check whether its pot bound - I have one of these and mine's developed dry brown patches on the leaves, largely because I haven't repotted it and the pot's way too small, so it can't hang on to enough water.