I used these guys to do an inspection on a house for me. Seemed fine, I guess. Hard to be certain though, because I wouldn't know there's any moisture they missed. 

I would suggest that it's probably good to use a company that does thermal imaging as well as moisture probing, but I'm far from an expert on the subject.

We've used these guys several times for builders reports and IR moisture reports - always excellent work

 - http://citylineir.co.nz/

I can't point you to a reputable operator but I do know of one case where an operator "highlighted" moisture problems in a property. The moisture was in fact the nails in the framing. So getting the right person is important.

If you have concerns then definitely get the professionals to test it and give you their opinion, BUT if you (a) want to do a quick test, (b) own the house and (c) have a multimeter with ohmmeter that measures in the tens of megaohms, you can do a bit of sleuthing yourself: with the probes 20-30mm apart, push them both 1-2mm into the wood, plaster or other material and check the reading. From my own experience an ideal dry reading in timber (eg, scotia, floorboard) should usually be over 20MOhm depending on material, if it drops down to 10-20 it's probably not too bad but you might want to look at reducing ambient moisture or eliminating sources such as by adding polythene moisture barrier under a raised floor.  If it's in the single digit MOhm or less then you almost certainly have a problem (or you were unlucky enough to hit a nail or something). Definitely YMMV, but it has worked for me.

Probe below the carpet line or inside a cupboard for an inconspicuous reading.  Take several readings by probing several times in the questionable area and compare these to similar materials in other parts of the house that are known to be dry.

I say you should own the house because I wouldn't want a tenant poking holes in my wall without my permission. And if there was even the slightest hint of a dampness problem somewhere it shouldn't be, I'd want to know about it ASAP.

Good luck!

Moisture meters as used by building inspectors cost circa $500. No doubt there are more and less expensive options available.