I have been trailer trash for a long time and patching a metal mobile home roof is preventative maintance. Every couple of years you need to use elastomeric roof coating or glop black stuff on the seams. When you use the black stuff be sure to use the stuff called cement not coating, the coating is thin and runny the cement is more like black cake icing (as mentioned above). There is also a fiberglass tape that can be used to make the repair much more durable. Layer of black stuff, lay down the screen and put down another layer of black stuff. Trust me this makes the repair last for years.

If the flashing is rusted out, you might be able to replace it yourself if you are somewhat handy with tools. The pipe would normally go through the roof, have a wide ring installed around the base (flashing), and be topped off with a hat. You will need to measure the diameter of the pipe, go down to your handy dandy hardware store, and buy new flashing and hat. While you are there ask the opinion of the proprietor there may be some new easy to install fix that i don't know about. Bring home the new parts, remove the old hat (cut it off or remove screws) put on the new flashing with lots of black cement under it, you might be able to add the new flashing without removing the old one. Then apply a layer of black cement and fiberglass to the area where the flashing meets the roof and then attach the new hat with a few screws. Be careful the edges of sheet metal parts are sharp, and work within your abilities. And above all else watch your step, it's not the fall that gets you, it's the sudden stop at the bottom that really hurts.