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Given that they have the ability to select pretty much whatever material they want with the transporters, I imagine it wouldn't be too hard for them to do a once a day transport for all dust/debris particles directly into space, or some containment unit of their choosing. Same goes for pretty much any other cleaning task.
It is mentioned in that one episode where they have a small village of “back to the land” type people staying in the cargo bay, along with their farm animals that they don’t have to keep sweeping up all the time, the bays will clean themselves. They just have to stop lighting cooking fires.
That actually makes me think, would it theoretically be possible to automate ship repair with transporter technology? All the time they have ships coming in with giant chunks missing.
If you are able to get a high resolution scan of the current state of the vessel, and have the plans to build it, couldn't they set up a specialized transporter to transport the damaged bits away, and transition area that is destroyed, and then replace it with new parts as needed?
Basically do some a similar repair method from Space Engineers, just fancier with transporters.