With radiation everything is always a trade off. You can have something which is very radioactive, but short-lived, or something that lasts millennia but is not very radioactive. Same for dissemination: you can have a small area heavily contaminated, or little background contamination on a very large area. You can't have both.
An airburst nuke would blow out a lot of surface, but produces little radiation, and very short lived. The plutonium of the bomb itself isn't very radiactive - it's far more poisonous than radioactive - and it will be spread in homeopathic amounts in a very big area. Hiroshima is a very big and beautiful city today (been there), and it's radioactive levels aren't anything extraordinay - in fact, lower than many other cities of the world.
An antibunker nuke would volatilize large quantities of dirt, concrete, steel and many other things, heavily irradiated, and blow it into the atmosphere. Since I know of no bunker made of cobalt, most of the irradiated isotopes created by the explosion will be either short-lived, or mildly radioactive. If they are blown to fall down on a large area, the quantities won't be significative, if they fall very much in the same place of the explosion, the dangerous zone will be quite small. As I said, you can't have both.
In short, you can have some very dangerous zones to grow vegetables, for a very long time, as long as they are small - and probably, quite easily detectable. If you want the whole globe to be irradiated... well, it already is, but the amount of extra radiation caused by all those bombs won't raise the background radiation level by more than a few decimal points.
EDIT: As per @Murphy suggestion, I'll clarify some aspects about alpha/beta/gamma emitters. The issue about cobalt-made bunkers is because radiation from a nuke could turn standard Co-59 into nasty Co-60, which is a very strong gamma emitter, with a relatively long life of little more than 5 years. That's really dangerous stuff. However, most of the byproducts of an underground nuke are going to be short (days) or medium (less than 5 years) alpha or beta emitters. Alpha radiation is mainly harmless unless ingested, but extremely dangerous if it's inside the body. However, in all of these cases, concentration is the key.