veneer question

That is the point, carpenter glue is the one that gets absorbed by wood product, be it a veneer or a piece of wood. In addition, you could barely see it, when it dries. You can also sand MDF if it's too smooth. I've seen some MDF is silky smooth. I've used carpenter glue on MDF a lot, and always succesfully.
thanks

In response to Mfkeleher's suggestion: If the veneer is varnished or laquered an iron will ruin the finish.

Get some "solid" glue (for glue-guns) and scrap off a small amount with a knife or razor blade. Then, gentle "tuck" that glue into the gap ("tuck-point" - like in masonry - BUT, DO IT GENTLY). Then take an iron (set between low and medium heat) and apply it to the veneer (keep the iron moving). When the glue softens (it will NOT take long), apply pressure for a minute, until the glue hardens. You will need use something to apply the pressure with (something that will cover the entire area - such as a piece of pre-cut wood. (Note: As stated by Mfkeleher, you may want to put something between the iron and veneer. A thin piece of soft cotton will be less likely to scratch the surface than paper).

I would absolutely not hesitate to use contact cement to repair loose veneer. To do it right you must apply it to BOTH surfaces and let it flash off. (let it sit until it becomes clear) Once it has flashed off the stuff will bond to itself like you wouldn't believe. A thin even application is all you need. A good idea is to cover any veneer in close proximity with painters tape in case it gets slopped around.
Good luck