I see Nelson and Buggs referenced this paper, Mol Biol Evol. 2009 Mar;26(3):603-12, by Toll-Riera et al. That 2009 paper analyzed ORFans in primates, concluding that the majority were similar to pre-existing genes and/or had sequences related to transposable elements. They were also able to track back a number of ORFan sequences to non-coding regions in the genomes of other mammals.
A PLOS Genetics article from last December (Ruiz-Orera et al, Origins of De Novo Genes in Human and Chimpanzee. PLOS Genetics, Dec 2015.) describes efforts to identify human- & chimp-specific proteins expressed by new genes. This is covers one area I think Nelson & Briggs mention where they wanted to see more work. Ruiz-Orera et al. also tried to identify novel RNA transcripts specific to these species. About half of the novel transcripts mapped to regions of previously annotated genes (introns & exons). Most of the others mapped to regions between known genes. For the latter, there seemed to be insertions of promoter sequences that would drive transcription from those intragenic regions. They found, as others have noted previously, that many of these de novo proteins seem have undergone limited purifying selection. An additional trait for many of the new transcripts is the codon usage, which have not come the distributions observed for genes conserved across species. These new genes (perhaps not coding a viable product in most cases) and expressed proteins also tend to be short, and for the genes, often have lower numbers of exons. These traits are considered indicative of very recent origin from previously non-protein encoding sequences. Larry Moran provides some additional perspective here.