Ask Mr. Smarty Plants

As far as Mr. Smarty Plants knows, Prosopis glandulosa (Honey mesquite) and all species of Propsopis have perfect, or bisexual, flowers with both stamens (male parts) and pistils (female parts) on the same flower.  Some other plants have separate male and female flowers on the same plant.  These plants are referred to as monoecious.  Still others have separate plants with male flowers and separate plants with female flowers and are called dioecious. Since mesquite trees have perfect flowers with both male and female parts, any mesquite tree has the potential to produce seed pods.  However, in some years the environmental conditions may be such (e.g., late freeze that damages flowers) that the plants don't produce a great number of seed pods.  Here is a link to more information about plant sexuality.

I did find a reference to a paper that says that Prosopis chilensis, P. pugionata, P. flexuosa, and P. forquata are andromonoecious, meaning that the plants have some perfect flowers that have both male and female parts and other flowers that function strictly as males.  Since there is a mixture of flowers on the plants, those flowers that still function as females would produce seeds. 

If you live near a university, you might be able to find a copy of the paper.  It is:

Hoc, Patricia S., Maria A. Agullo, and Ramon A. Palacios.  1994.  "Stylar trimorphism in four functionally andromonoecious Prosopis species (Mimosaceae)".  Plant Systematics and Evolution 190:143-156.