Older Home: Condensation Problem: Walls? I bought a 100+ year home which has electric baseboard heaters. Throughout the...

I bought a 100+ year home which has electric baseboard heaters.
Throughout the winter, there be condensation on both the main story and the upstairs -- especially on the walls near the ceiling. In some places it gathered and started running down the wall.
Mold has formed surrounded by one wall in the house. (roughly 1 sqft in size) Bleaching it away doesn't comfort and it comes back frequently. Unfortunately I live in a cold climate, so space the windows during the winter won't work.
Dehumidifiers do not work, even when constantly on.
It does appear that the house suffers from a lack of insulation within the exterior walls. The windows are vinyl.

How do I stop this excessive condensation? Should I better insulate the walls? The attic? How do I know that this would help?
if your dropping heat to save money this may be problem the radiator the air the more moister it holds the colder the temp is in the house the moisture will collect on the walls also variety sure you have a fan that vent to outside in both the bathroom and kitchen i would make sure the attic is insulated boil rises I would do the walls as a last resort pickme is on the right track. Warm air holds more moisture than cold nouns. What's happening is a like a chalice that has a cold drink in it. The moisture contained by the warm interior air is condensing on the cold walls.

Insulating walls & attics would be the first step, and will probably solve the problem (as ably as lowering your heating bills).
I would look for a hose leak somewhere in the home. Normally, running a heating system will dehumidify the home. As the temperature inside rises (in comparison to the outside temperature) the relative humidity in the house falls.

For example, if the warmth outside is 40 degrees and the humidity is 60%, inside a 72 degree house the humidity will be just 19%, which is very dry.

Consider buying a humidistat and monitor the humidity in your home. If it is constantly illustrious (over 40%-50%) regardless of running the heater or A/C there is probably another issue contained by the house.
Answers:    When walls are cold they will hold water condensing on them. Better insulation will keep the walls from getting colder. However, you said that the walls appear to be satisfactorily insulated. Some simple things that I can think of that would cause as much humidity within your home as you are descirbing would be:

1) Clothes dryer not vented to the outside of the house.
2) No exhaust fans surrounded by the bathrooms
3) No exhaust fan in the kitchen
4) No attic vent
5) Leaky roof

I would check those in that order.

I am curios that you mentioned the walls and not the window because I would think that you would see condensation on the windows first. If you solely see it on the walls and not on the windows then I would enjoy an energy audit done and make sure they use an infrared camera while doing it. The infrared camera can detect gap in the wall insulation which may be causing cold spots.
Your vapor barrier may hold large holes or gaps, or may be nonexistent Come on 100 years prehistoric home it's a luxury for the history museum.