I just did something similar - attached squares of 1/2" plywood to an
interior door (I was actually making a table, but the principle is the
same). To attach the plywood, I sanded any finish off the door, used
wood glue to attach the ply to the door, and a bunch of countersunk
5/8" wood screws to hold the ply on while the glue dried. Clamps would
have worked too, but I thought a bunch of screws would distribute the
pressure better. Some of the screws stripped the soft wood on the door
"skin" pretty easily, but most of them held the ply on tightly while
the glue dried. There's so much glue area I'm not worried about
whether the screws hold long-term. If I wanted to mount something like
a spice rack that I might want to remove at some point, I'd glue/screw
a piece of plywood to the door, then attach the rack to the plywood.
Good luck,
Andy