Running Viewshed on one feature at time in shapefile?

I've never used the viewshed tool so I can't speak to the specifics of using that tool, however in regards to your suggestion in this question I will add an answer here to build on KHibma's solution.

The first thing we need to address is the format of your SQL query: "[OID] = count". As it stands, this query will fail since "count", as represented here, is a string and strings need to be surrounded by single quotes: "[OID] = 'count'". Now, the second reason this query will fail is that OID is an integer field and as such there will be no OID value equal to "count". This is where string formatting comes into play: '"OID" = {}'.format(i) or '"OID" = {0}'.format(i) for those using Python 2.6.x (Use quotation marks to enclose the fieldname when using a shapefile. See ArcGIS help.).

To avoid certain pitfalls of making queries on the OBJECTID field, we can nest the loop into a cursor to make sure that we are only querying OID values that exist:

arcpy.MakeFeatureLayer_management ("C:/data/pts.shp", "pts")

with arcpy.da.SearchCursor('pts',['OID']) as cursor:
    for row in cursor:
        oid = row.OID # or whatever your OBJECTID field is called
        arcpy.SelectLayerByAttribute_management ("pts", "NEW_SELECTION", '"OID" = {}'.format(oid))
        outViewshed = Viewshed("elevation","pts",2,"CURVED_EARTH",0.15)
        outViewshed.save("C:/sapyexamples/output/outvwshd"+oid)

OK, borrowing from the answer from @Jason, I was able to tweak it a bit to finally come up with a script that works great. I also switched it to use FID instead of OID. Either way, it will work.

arcpy.MakeFeatureLayer_management (inPoints, "pts")

with arcpy.da.SearchCursor('pts',['FID']) as cursor:
    for row in cursor:
        fid = str(row[0]) ### Must be string
        print fid
        arcpy.SelectLayerByAttribute_management ("pts", "NEW_SELECTION", '"FID" = {}'.format(fid))
        outViewshed = Viewshed(inDEM,"pts",1,"CURVED_EARTH",0.15)
        outViewshed.save("C:/Python/output/viewsheds/"+fid)

Perhaps this will help someone in the future. Thanks everyone!