Not quite sure why you'd want to pay to have somebody come on board and throw litter all over your ship, but it takes all kinds. Personally, I'd rather the trash accumulated naturally over time, so the ship looks more and more "lived-in" the longer you actually live in it and don't dock somewhere. An exploration ship just back from the proverbial five-year voyage should look as awful on the inside as it looks on the outside.
But a semantic point on the above: the trash isn't going to "roll around at your feet". Your ship is in zero G whenever it's not accelerating or sitting on or near a planet. So it won't "roll around on the ground", it will "float about the place". Which could be anywhere from mildly annoying to disastrous, if it happened to randomly float up and obstruct your cockpit view and/or instrumentation screens.
Though that could be an answer to the "reverski problem": if accelerating backwards made all the trash in your cockpit fly forwards and land on the cockpit in front of you, obstructing your view.