Hi Gootzie.
Let me give a general response about screen size, then address your specific concerns.
We have two screen sizes, standard and superfine.
If you are only going to be using a clay based scoopable litter, (they will always say "scoopable" or "clumping" on the package) then the fine screen is better at filtering out small clumps that can occur when a cat digs and breaks up what would be a single clump. Therefore, the litter stays cleaner and fresher smelling. The downside of the superfine screen is that it cannot be used with alternative litters such as World's Best Cat Litter, Litter Pearls, and Swheat Scoop.
If you use an alternative litter such as the 3 listed above, you need to order the standard screen to accomodate the larger grain of the alternative litters.
The screens can only be changed at the factory, so the best thing to do is try and decide what litter type you will use in advance.
As for your concern about your cats not covering their waste, the solid waste is coated by litter as the globe slowly spins, so the waste is not hitting the globe wall and smearing the interior. The exception might be Litter Pearls which I don't think stick to the waste. Perhaps a Litter Pearl user could comment better on this.
On an unrelated topic, I can tell you that if you have a cat that likes to dig, you should definitely order the Kick'n Kitty Guards. They keep the waste ports covered when the globe is in the home position and this keeps the cat from kicking litter out the side of the unit.
In short, I'd say that if you are sure you won't be trying alternative litters, get the fine screen. If you are using alternatives or think you may want to try them, get the standard screen.
Please note that the Litter Robot is NOT compatible with non-clumping clay based litters with either screen. Feline Pine is also not compatible with the Litter Robot because the pellets are too large to fit through even the standard screen.
If you have further questions, please feel free to contact me. I can be reached by emailing
mailto:info@litter-robot.com.