The advice on RCD is very good. Use a good piece of wire between Dishwasher casing and sink to try to trip it (and wear gloves just in case). I would also run an extension cable from another part of the house, and use the EARTH on that to measure the dishwasher against (in case there is something wrong with the sink or the whole kitchen's grounding).
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We are so used to digital multimeters nowadays that nobody has much regard for impedance and the way these things work:
Impedance is the AC equivalent of resistance, the only difference being it usually varies with frequency (of the AC). You could alternatively think of resistance as a special instance of impedance. But I digress slightly...
In the old days when meters had needles that waggled, the coil in the meter had an impedance, and needed some current flowing to make any sort of "voltage" measurement*. The finer the wire of the meter coil, the higher the impedance, and the less flowing current was necessary (generally speaking).
Modern digital multimeters (DMMs) tend to have huge impedance (when measuring voltage) and tiny currents flow (almost nothing at all). This can give you truly weird readings sometimes. In particular, DMMs can show "dangerous" voltages where there's nothign dangerous in practice. An example is getting sparks from a comb or hairbrush in the dry winter mornings - the "static" electricity can be high voltage, but there isn't enough charge on the brush to cause a dangerous current to flow. That said, you can still feel it, and a DMM should show quite a high voltage, although probably only for a moment or so. I have heard of people being killed by electricity whilst playing golf (especially in Florida**), but never from brushing their hair!
This is NOT to say your 'leccy system is OK, but that you have to do a bit more than just apply a meter to be sure it's safe. Testing with an RCD cutout is a really good idea, as a starting point. Also you are assuming that the dishwasher is at fault, and not something causing the sink to float up to a higher voltage than ground. Admittedly my money is on the dishwasher, but you have to be systematic and careful when checking this stuff.
Too much info, per usual, but it might be helpful.
E.
*Moving coil meters can't measure voltage directly, but they measure the current through a given resistor and use Ohm's law to get the voltage. DMMs in contrast, pretty much measure voltage (over-simplification I know). It does lead to different readings in the same conditions though, so you need to understand if you use both types. DMMs can't measure current directly, so they measure the voltage across a known resistor (over-simplification!).
**Lightning strikes: If you also account for Alligators, apparently, Florida is a dangerous place to be a golfer.
