If you click on the red question mark next to the specificity column in the GOMo output, you'll see the following definition:
A measure of the relative position in the GO hierarchy showing how specific a term is. A value of 100% implies that the GO term is the most specific form whereas a value of 0% implies that the GO term is one of the three roots of the Gene Ontology with only terms below it. A tilda (~) infront of the percentage implies that the value shown has been rounded and is not exact.
So yes, you should definitely consider the specificity. The lower the specificity, the less useful the associated GO term is likely to be.
GOMo creates a list of genes ordered by increasing affinity of the motif for the region upstream of the gene. The ranking number is the position of the gene in that list. That is, genes with lower ranking have less affinity for the motif.