First I must admit I know next to nothing about Peperomia.
That being said, this past winter I spent some time propagating 108 plants to share and yes, some of the plants developed brown spots. Since I had no clue, I just pulled off the affected leaves and discarded them.
I did a quick bit of research and (I can only guess at this part) it may have been Rhizoctonia leaf spot which is something that happens to some Peperomia varieties.
Here is the wiki page for diseases of Peperomia:
Hopefully an expert will come along with a better answer for you.