Melted poly on top of an electrical boxes (light fixtures, outlets, ceiling fans) is a sign of trouble. Have an electrician inspect the installation to ensure it is safe. You can help by ensuring the light fixture below has the appropriate bulb and wattage to help reduce the chances of over-heating. This overheated fixture is also a source of warm moist air into the attic and should be sealed.
Soffits are designed to allow air intake into the attic space. If they are blocked for any reason the intake ventilation must be created through Roof intake vents. These are vents installed on the top of the roof but down near the Eave edges. They must be installed on both sides of the roof to balance. This is now common practice in New construction.
Attic batt insulation should not be block the edges of the attic space and hence restrict air intake flow from the soffit areas. The attic batt insulation should be pulled back to allow an air space above, preferably with the aid of a cardboard stop (installed at time of construction) or retro-fitted with a styrofoam Air Chute.
Bare spots in the attic insulation can cause temperature variations within a room below but are also a prime culprit for Ice Damming on the roof above. Excessive heat transfers through the ceiling and up to the roof above. This localized heat can cause the under-side of the snow pack on the roof to melt only to later freeze. This cycle builds resulting in an Ice Dam. Ice Dams damage shingles and can lead to leaks. Under-insulated attics are often easy to address and can be a quick and cost effective improvement to your attic insulation problems.
A bathroom fan vent pipe must be properly insulated to prevent condensation. Breakdowns like this can create moisture that will travel back into the living spaces and cause damage.
Water damage on ceiling drywall isn’t always due to a roof leak or insulation issues. Sometimes the work of other trades in the attic fails and causes additional moist air that is not properly ventilated. It’s a good idea to poke your head into your attic at the first signs of water damage on the ceiling.