I haven't house-sat, so I don't know about the cleaning level. I am slightly boggled by the idea of a house where you can't find a broom or dust pan - how many places could you potentially store those, after all? (If they don't own one, I'm guessing they won't expect stellar cleanliness.)

About the cat litter, if you don't find a broom, you could try vacuuming, depending on how good their vacuum is (if you can find one) and how it fits in the bathroom (or wherever the litter pan is). Barring that, you could try wet paper towels- if the litter is clay based or clumping, it should stick to them with a little pressure.