What happens if you select one one of the face markers closest to the split line? Does it highlight the faces on both sides of the line? If so, then it's most likely not a split polygon problem but an earlier extrude problem or something. So, if clicking on the dot closest to the split line highlights both sides of the line, it's selecting one face (a face that wasn't split.
If so, then before you did the split, you had two faces directly on top of each other. When you did the split, you split the foremost faces. When you goto face select mode, your seeing the two faces you created from the split and the one unsplit face hiding underneath. I say that because the bottom face that isn't split has a dot in the middle that's lined up with all the extra dots above it.
If you want confirmation, select the bottom face that isn't split and delete it to see if another face takes it's place.
Sorry for being so wordy, brains not working to well today and wanted to make sure I explained good enough.
Don't be satisfied with what you can do but rather strive to do the things you can't do!