It's a very bad paper. That is the short story. I haven't thought through all my criticisms of it yet (maybe I'll write something here eventually). In the meantime, I like this overview piece at Climate Central by Michael D. Lemonick [LINK]. I especially enjoyed the comment that, "... it's not that NASA data are blowing a hole in anything. It's that Spencer's interpretation of NASA data are blowing... something, somewhere."
For those of you looking to actually read the paper, it is in a journal called Remote Sensing, and it is open access. You can find it by looking up doi:10.3390/rs3081603. Let me reiterate that this is a bad paper, with many incorrect statements, assumptions, and reasoning. It isn't worth you time reading this paper when you could better spend it reading an informative one about climate sensitivity... oh, I don't know, maybe doi:10.1175/2008JCLI1995.1