It's pretty simple to see in this picture what is wrong. It looks like after the roofers were done, they left their propane tank and garbage on the side of the skylight. Very poor decision making, not to mention dangerous.
In the picture below, it's evident that a skylight was ordered that was much too big for this opening. I'm guessing they got the skylight on sale and wanted to save some money. The problem here is that dead air is now all around the inteior of the skylight. Dead air will create condensation issues. This skylight has been creating condensation issues for years.
The problem here is the exposed wood. There was a metal flashing protecting/covering the wood, but underneath, an ice and water membrane was never installed.
Let's re-visit this picture, but take a closer look. Rather than installing a proper membrane, these installers threw a bucket of tar on the curb. That tar is 4 inches think in some spots. What a terrible idea for sealing a skylight.
This is a self flashing skylight that has exposed nails. The bigger problem is the caulking around the skylight. There is a built-in condensation gutter that will allow the condensation to exit from inside the house to outside. Since the gutter is caulked, the water cannot escape and is running down the homeowners' drywall. (NEVER CAULK A SKYLIGHT ON THE EXTERIOR.)
This video speaks for itself. I recorded this at a client's home and you can see how much water was inside the unit.