A leaf spot. Perhaps it was there prior to plantng but you didn't notice it?

What's the plant's name.
And where do you live?
Prevailing temps?
Any rain?

I am in SC. Zone 8. Temps have been daytime 70s nighttime 40s and 50s. One day of soaking rain, otherwise mostly sunny.

I don't know the name of the shrub. Maybe it is red-tip photinia?http://www.clemson.edu/extension/hgic/plants/landscape/shrubs/hgic1081.html

I guess going by what the extension says, maybe I should get rid of the sick plant before it infects its neighbor.

With photinia, leafspot is a standard condition.

Looks more like Indian Hawthorn to me (Rapheolepis indica), for which leafspot is a standard condition.

Next time...don't use compost or anything else in the planting hole. Plants do better when placed into the natural soil.

SCurbanyard 8, This came to mind.