Most things on a boat are designed to withstand water damage and stains pretty well, and one of the ways this is achieved is by using vinyl. Unfortunately, exposure to sun and water over time can dry out and crack the vinyl, and the attempt to make it look like leather can create pores and creases that will collect mildew. Fortunately Vinyl is very easy to clean!
For most common stains and mold spots, standard bathroom mold and mildew spray will work. These cleaners were designed to work on common vinyl flooring in bathrooms, so they won't hurt the vinyl. Spray directly onto the dirty areas and allow to sit for several minutes. This will ensure the spray loosens the mold and grime. Wipe with paper towels, then wipe down the seat with a wet cloth to remove leftover residue. This should remove most of the dirt and stains.
Mr. Clean Magic Erasers These "magic erasers" are essentially a very mild abrasive material with a cleaning agent contained within. This can be used to absorbe more stubborn stains. There is no residue left behind and there is no rinsing required. The abrasiveness is so mild that there is no chance of damage to the vinyl. Use these on any stain that persists after cleaning with bathroom cleaners.
Condition your Vinyl!!!
In my experience 3M makes the best Marine Vinyl conditioner and it is pretty affordable too. The conditioner will rejuvinate old and faded vinyl as well as create a layer of mold resistant protection.