What was that!?
Looks as though there are two problems there.
One is certainly that the probes aren't conducting as reliably as they should - whether they're dirty, covered in oxide or whatever. I had a very similar experience with a set of probes from Maplin a few weeks ago, and took them straight back as unfit for purpose. Life is too short for test equipment that doesn't do its job properly.
The other I suspect is down to how the autoranging feature works in the presence of an inductive load. I can see a way in which it could start oscillating, which would prevent the meter from ever reaching a steady state.
Suppose the meter applies a small voltage and tries to measure the current. The coil is inductive, so initially very little current flows. The meter detects this as a high resistance, so switches up to a new range. Meanwhile, the current in the coil is ramping up (V=L dI/dt). The coil current is now too high for the high resistance range, so the meter switches back to a lower resistance range, with a smaller applied voltage.
I wouldn't like to speculate on exactly how the oscillation is maintained, but I can well see that a meter's autoranging algorithm might work on the assumption that the thing it's measuring has a fairly constant resistance - but in this case, it doesn't. The current in the coil doesn't just depend on the applied voltage, it also depends on how much energy is stored in the coil's magnetic field.
Result: one confused meter, until it's stuck in manual mode which disables the autoranging mechanism. Given a constant applied voltage (or current) for a while, the inductive ringing dies down and the meter is able to report the dc resistance correctly.