I have 2 questions, as a expat and new parent residing in Shanghai (2000km from Fukushima) where we are now experiencing radioactive fallout from the Fukushima Nuclear Plant (Japan), we can not get any 'real' infomation about what are safe limits for food and air. We simply do not understand the reports we are given, nor the poor explanations that accompany the reports, which are written by design to try make people feel safe and not panic. In fact, we have no idea if the numbers being released are even true. What we are being told is that yes there is fallout and some vegetables have had 1-3 Bq/Kg detected on them, i.e. spinach. And for Air in Shanghai today (mBq/m(3)) 131-I (.58), 137Cesium (.17) and 134Cesium (.16). Now I know -from what i have learned -no one can give me specifics and certainties with all this, but what are we looking at here? Can any of you geniuses in this community - and I say this respectfully-- tel me if these levels are dangerous? Would appreciate your advice...
First, just recall that one becquerel is one radioactive decay per second.
If your spinach has had 1-3 Bq/kg, then you should just completely forget about any threats - there is no danger whatsoever. The safe limits are 100-500 Bq/kg, see e.g.
which are 100+ times higher than what you report. Of course, I can't completely eliminate the risk that your next package of spinach will be unchecked and will contain 1/3 of the weight stored in plutonium :-) but it is unlikely because things are being checked.
To compare, an average (healthy) banana - because of its potassium content (radioactive potassium-40 is 0.01% of natural potassium; it decays to argon-40 with half-life 1.25 billion years) - has about 15 becquerels which is like 5-15 kilograms of your (not so) "radioactive" spinach. That's despite the fact that the average banana's mass is just 120 grams! Because of its measurable radioactivity content, a "banana equivalent dose" is sometimes used to compare radioactivity with the exposure in normal life - and this is an example where the comparison is useful. Potassium-40 is the main source of radioactivity in humans, beating even carbon-14. The conclusion is that the spinach is not radioactive in any practical sense of the word.
The radioactivity in the air is negligible as well. The U.S. limits are about 150 becquerels per cubic meters, so if you tell us about some isotopes contributing less than one millibecquerel per cubic meter, which is one million times less, there is really nothing to talk about - as long as they mention isotopes that are relatively short-lived (and assuming that none of the data and units have been misinterpreted).
If one got the same amount of becquerels from plutonium which has a much longer half-life, one would need much more plutonium (by mass) to explain the data, and this plutonium would stay in your lungs forever - it is dangerous. But millibecquerels per cubic meter stored in short-lived isotopes are totally irrelevant and chances are that the numbers don't differ from the natural background in Shanghai in any recognizable way.
Many of those quantities are actually within the safe levels even a few miles away from Fukushima, so if your distance is thousands of miles, be sure that the effect of the hassles in Fukushima is between inconsequential and undetectable.
Pretty much all the hysteria is completely irrational and scientifically unjustifiable.
A Bq is a Becquerel or decay rate of 1 event per second (on average, because this is different from Hz which is events coming 1 second apart like, well, clockwork). Note in the chart anna posted the dose from cosmic rays, that comes from an event rate rather more than Bq.
How much radioactive dose that is depends on how it is delivered. From Iodine-131 it is $\beta^-$, which (a) does not have a lot of penetrating power (good while it is outside you, not so good once you ingest it) and (b) how a quality factor of 1 (a nice low value).
Iodine however, poses a special risk if you ingest it: it gets collected in the thyroid glands, which means that the dose (and the risk) is not spread out all over, it is concentrated in one place.
But one quick comparison: banana, spinach, etc. naturally have a lot of Potassium, and that means some Potassium-40 which is also radioactive. A typical banana carries several Bq of K-40. This is the source of the dose from eating a banana in the XKCD link that anna gave you. (I've used this fact to demonstrate high sensitivity gamma detectors to visiting VIPs because it does not require any of the paperwork associated with radioactive test sources: just put your lunch in the detector.)
So the risk you're hearing about now is not large. Pay attention to the reports (to learn if things change), consider eating a little less of the affected foods, and don't fret it.
To supplement Lubos' answer, this graph gives numbers and put things in perspective.
Note that just sleeping next to another human you are exposed to some radiation. The table uses sieverts, which is the way the cumulative harm of radiation is measured on human health.
There exists always a background level of radiation, from the ground and the air and the cosmic rays. The numbers you are quoting are within the statistical error in your region, so no, it is not dangerous.
One Bq is defined as the activity of a quantity of radioactive material in which one nucleus decays per second. You have to realize that as we sit or sleep or do anything, one cosmic ray per minute per cm**2 passes through us at sea level and is about half the natural radiation count level. That is what I mean when I say the numbers you are quoting are within the error of the ambient radiation.