Prestidigitations are minor tricks that novice spellcasters use for practice. Once cast, a prestidigitation spell enables you to perform simple magical effects for 1 hour. The effects are minor and have severe limitations. A prestidigitation can slowly lift 1 pound of material. It can color, clean, or soil items in a 1-foot cube each round. It can chill, warm, or flavor 1 pound of nonliving material. It cannot deal damage or affect the concentration of spellcasters. Prestidigitation can create small objects, but they look crude and artificial. The materials created by a prestidigitation spell are extremely fragile, and they cannot be used as tools, weapons, or spell components. Finally, prestidigitation lacks the power to duplicate any other spell effects. Any actual change to an object (beyond just moving, cleaning, or soiling it) persists only 1 hour.
This is how the cantrip is described and yet it leaves a bit to the imagination. This could be why there are so many threads on the subject. I have seen some things come up now and again in these threads, but never did I see a firm answer, so here is the question.
If the spell allows you to continue using it for an hour, stirring, heating, cooling and cleaning, what about items you created with it? Do they simply vanish or do they stick around?
Finally a special question. Soiling...would it or could it be considered dying something with color? As an example, an image the caster sees or imagines 'printed' or 'soiled' onto a parchment.
Since the spell lasts an hour and can be repeated unlimited times, I would suggest that there's no harm in treating each application of prestidigitation as a new one hour instance of the spell.
You can colour things, but it can only do so crudely. Imagine magically controlling a crayon that's a foot across and trying to write with it. :P
Items created vanish after an hour, they aren't one of the permanent exceptions mentioned. Now as far as soiling is concerned I believe it is literal. You are covering something in actual dirt and grime. Just coloring something is temporary and lasts only an hour.
Unfortunately it cleans or soils whole items, so you can't really form letters. You could rearrange existing dust though, that should do the trick.
So what happens if during a social encounter you use soil on someone elses clothes?
That person is going to be wearing dirty clothes if they fail a saving throw. It doesn't specify when or which save is appropriate. But in this case since the item targeted is worn by someone I would grant a save vs the soil effect, reflex save seems to be the most appropriate. Also they are going to be very angry with you... Not recommended to use this in a social encounter unless you are trying to make enemies.