I don't understand why Kishi didn't just give Sasuke two rinnegans instead of just one. If i'm not mistaken he still has his sharingan abilities locked into his new Rinnegan (so those abilities won't go away) and if he had two instead of one he wouldn't look so derpy.
There is no explanation for that, Ultrapain. Madaras Rinnegan had also the abilities of the Sharingan because the Rinnegan is the peak of the Sharingan.
You can also forget the explanation regarding the moon-seal. That only his left side could have that power. That's nonsense, because the Rikudō no Yin no Chikara(that's the name of Sasukes seal)doesn't have to do with Sasukes Rinnegan, it's independent.
The author does what he want. He doesn't care for any former regularities.