I can tell that you transplanted your palm into a larger container and raised the water volume. The increase in water will drown the roots so be very careful not to over water. Water thoroughly but allow soil to dry slightly between waterings. Use your finger to feel the soil before watering and let the top inch dry before watering.
Like other palms, the areca needs filtered light, preferably near a southeast or west-facing window, so place your palm tree in bright, indirect light. The spots are caused from environmental conditions "over-watering" and when you get it settled they should go away.