How do you keep the leaves of an indoor plant clean and shiny? Do I have to scrub each one?
yes.
the alternative is to buy those gloss solutions for plant leaves that come in a spritz bottle. you can get them pretty much anywhere they sell potting soil (walmart garden section?). it leaves the leaves really shiny but seems like it might be bad for the plant. don’t know if any plants have those breathy holes on the top sides of their leaves, but random chemicals deposited all over it can’t be beneficial…
Thanks
And by “scrub”, I hope you mean “mist with a water bottle and gently wipe clean” since that’s all that’s required 
Stomatal pores are located on the underside of the leaf so I don’t see the harm in using a leaf gloss. I never have, but I doubt it’ll hurt a plant any more than the usual mistreatment most houseplants undergo.
I’ve had good results using a tablespoon of milk mixed into a glass of water, applied with a ball of cotton wool.
Alternatively, if it’s a nice warm day, take it outside and gently spray it with a very fine mist from the hose (not all plants will appreciate this, but most of the really robust types with glossy leaves won’t mind it at all, just as long as you don’t leave them wet outside if it is cold or windy).
In Germany, I saw people using mayonaisse (very lightly) on larger leaf plants. They swore it was also good for the plant.
Works on BLT’s so who knows.