Looking at the new responses I'm tempted to try the Chinese based tester like here - http://www.ebay.co.uk/itm/131254208134 if someone can confirm it is suitable to test capacitor ESR in-circuit. The lower price is better for me, means I can spend elsewhere getting some more equipment, I only need to know if they are bad, not how bad - just replace yes or no, the measurement being somewhat accurate is fine, doesn't need to be a precision part.
That looks good to me, it has a crystal and looks the ATmega328 is a dipp which means easy to replace or upgrade. Seems to have external power as well. According to Madires as he mentioned both the lastest K and M firmware supports in circuit testing.
In order to update the firmware you will need to add an ISP header and get a USB to ISP programmer, or program an ATmega328 externally then drop it in, if doing this a socket will help.
All these parts are dirt cheap on ebay (as well as other replacement parts), you should be able to get both for around £10 delivered, then use them to program other arduino projects as well.
In circuit testing isn't 100% conclusive as you have parallel caps and resistors and it will throw your measurements off. But if you see a few of the same caps in parallel you can make an estimate from the cumulative ESR.
The AVR/Chinese testers will not discharge the caps (if they have a charge). The Peak Atlas will only discharge to about +/-50v as well. So any larger caps you will need to check and discharge manually.
One other thing is auto operation, (afaik) AVR/Chinese testers will require you to press a button while the Peak Atlas seems automatic.
You can probably build your own AVR tester on a prototype board for about £10
Download this GNU tarball and take a read of ttester.pdf it also has info on the Chinese clones.
http://www.mikrocontroller.net/svnbrowser/transistortester/Doku/trunk/pdftex/english/I have 2 of the Chinese ones I picked up for about £20 (without a case) and also a bench LCR meter that was about £50.
You may have already seen this. Not sure why he ran into problems but without inspecting and updating the firmware you could be buying into a Chinese issue rather the a problem with the original AVR design, anyway it's a very simple circuit.