You should understand the difference between “radiation” and “radioactive contamination”. You won’t find “radiation” on vegetables, or on anything else for that matter, which is not either a natural emitter of radiation, or pretty highly contaminated with radiation. And in the case of a “natural emitter”, the radiation is inherent in the material.
So, for example, a radioactive source, such as Cobalt-60 or Iridium-192 (both industrial materials used in the nondestructive examination of welding), “emits” radiation, because those materials are radioactive. But when an NDE technician examines a weldment by exposing the radioactive source to it in order to capture a film image of the exposure, and then re-houses the source in its shielded container, there is no “radiation” found on the weldment. That is, the source is encapsulated for the entire time of its use, including when it is exposed to the weldment, so that no particles of it remain behind after use.
However, otherwise non-radioactive materials (including metals) can become radioactive through long-term exposure to high levels of radiation, or simply from being rubbed against a radioactive material and retaining some of that material. (If iron were radioactive, for example – and it’s not – then “rust” that you can get on your hands and clothing would represent “radioactive contamination”.) That’s why many materials and surfaces inside nuclear plants (including even the dust and water) can become radioactive, because they are “radioactively contaminated” by virtue of their exposure to radioactive materials.
Radioactive contamination is a problem in the immediate vicinity of the Japanese nuke plants because their containments have been breached to some degree and because they have been releasing contaminated gases and liquids in order to relieve the pressure buildup inside the containment vessels. Radioactive contamination is a potential problem at any operating nuclear plant, and most do a very fine job at detecting and eliminating exposures and leaks.
It’s unlikely that measurable levels of contaminated dust or liquid from the Japanese plants would find its way across the Pacific Ocean to California accidentally. Please note both qualifiers in that statement: “measurable” and “accidentally”.
There is natural background radiation detectable nearly everywhere on Earth. (You may find some deep caves where cosmic and background radiation are nearly nil, but you won’t be living there.) Since radioactivity varies so much by elevation (there’s more cosmic radiation at higher elevations than there is at sea level) and by geology (granite is naturally radioactive at low levels, and so are concrete and coal), and isn’t a perfectly measurable quantity in any case, it’s going to be hard to detect “new” radiation from “what has always been present ‘here’ (wherever ‘here’ happens to be)”. That addresses the issue of “measurable”.
And it’s always possible that someone could deliberately spread radioactive contamination in an area in order to further some Luddite agenda that we should shut down every potential source of man-made radiation / contamination. But that wouldn’t be accidental.