The black streaks come from water running off your roof and removal depends to some extent on what sort of dirt was in the water. In areas where there are industrial wastes (smoke, petroleum residue, etc) in the air or acid rain, removal can be VERY difficult. In other areas it isn't too bad but still requires a heavy duty cleaner or automative/boat type cleaner and polish (not just a wax). The good news is that the painted aluminum siding on your trailer is pretty much impervious to anything short of aceton, lacquer thinner or brake fluid. It can, however, be scratched by arasives such as Comet cleanser. If you can't find the Korkay that Jim recommends (excellent product), try some other industrial grade cleaner/degreasers or heavy duty household products like Simple Green. Fiberglass boats often suffer from water borne streaks and smudges and I have found that boat cleaner/polishes often work well to remove surface grime from both painted and glass RVs.
The vinyl moldings do get moldy and are darn near impossible to clean up. The best solution is to simpy replace it - it's not too expensive. The domed vinyl strip just pops out of the metal track and a new one is inserted by folding the new strip slightly and pressing it into the track. For attempted cleaning, I've used a cloth moistened with lacquer thinner with some success but you must be very careful to avoid getting any on the sidewalls or any plastic surface. Bleach ought to kill the mold but it doesn't seem to get ii out of the pores, so you are left with discolored vinyl that is gray instead of black.