Oh dear, I find these plants impossible to keep in good condition for any length of time. Here's what you're supposed to do - they don't like to dry out, although that doesn't mean they should be left standing in water, it means they need frequent watering and the compost should feel damp but not sodden at all times. They also like high humidity around them, so central heating is its worst enemy. Stand away from any heat source, and use a pebble tray ( a tray larger than the pot, fill with pebbles, half fill with water, stand the plant pot on top so its not sitting in the water) to try to increase humidity around the plant's leaves.

Anthuriums also need plenty of indirect light, and what you describe could also mean that it is too far from the nearest window. I would also do what Bamboo said, since the two problems certainly aren't mutually exclusive.
In feeding, the watchword is "weakly, weekly", as with orchids. Anthuriums prefer frequent, light feedings, with a low phosphate plant food.
Keep an eye out for mealybugs, which appear as tiny, fuzzy white blobs next to the leaf veins, or where the leaf stems join the main stem at the base.