A few posts earlier I wrote about the kind of accuracy that can be achieved in the field with various types of compasses. 2-3 degree accuracy is achievable with a mirror compass. Most of the time it isn't really necessary. Sometimes however, it is - and unless you have a working GPS at hand, a precision compass is the only tool that can help you out.
10-degree accuracy, which you've been referring to in your last post, would be a very poor performance by anyone's standard. Translated into mils, that's 178 mils or a deviation of 178 m at 1 km / 1.8 km at 10 km. More than enough to miss your mark completely in any kind of difficult terrain and/or low visibility.
For any kind of precise "triangulation" (I assume you actually mean resection) you'd need a highly accurate compass. Ideally a prismatic one, such as the British Army issue Francis Baker M73:
http://www.ravenlore.co.uk/html/prismatic_compass.htmlThese are very expensive toys, but note that they're not fitted with a spirit level or even a tripod mount. BTW, I've never had any issues using a compass on steep slopes. The magnetic needle itself is a good enough indicator if you're holding the compass level - if not, the needle won't swing freely anyway and it will be impossible to take a bearing.
As for a tripod mount, I can't see any utility in that unless you're a land surveyor using a professional surveying compass (the $5 eBay special isn't going to cut it). Keep in mind that pretty much any photo tripod out there uses a steel screw to secure the camera. Not exactly a good idea if you intend to mount a compass...
P.S.: If you want to check the accuracy of your compass I would recommend a better method instead. Go some place with a clear field of view to easily identifiable landmarks (such as mountain tops) as distant as possible. Take bearings to each individual landmark. Now take a good map (Google Earth works, too!), identify your location and measure the angles to each landmark in question. They should correspond more or less exactly with the bearings taken with your compass, correcting for the magnetic declination obviously.
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