Yes, that's the difficult point: to get all the radiation in, and the thermal stability under control.
Dependence on the position of the beam, and uncertainties due to internal reflections/inhomogeneities is unfortunately unavoidable, but I think this is even worse with photodiodes.
Many commercial laser and microwave power meters in the range ~0.1-300mW work in this way, the advantage being
not sensitive to wavelength
(eg microwave power meters can typically cover 100khz-18Ghz in this way). Usually one has a wheatstone bridge or two and a reference thermistor in the same case for temperature compensation. Such a thing is sensitive to temperature differences of a fraction of a degree, and the accuracy can be below a percent.
For inspiration see chapter III and especially
Fig 3-2 on p 21 of:
http://literature.agilent.com/litweb/pdf/5965-6630E.pdf
(it's 2.5MB, watch out).
However they use very delicate constructions that a hobbyist won't be able to build.
Obviously the problem gets more difficult when trying to measure small powers, lets say less than a few mW.
I personally like to aim for something that would work until a few 10's or 100's mW. There are various sorts of thermistors available (I checked the data of the Epcos thermistors sold by Farnell), and the main part would be to play with a few of them to
see which works best and especially how it should be thermally mounted. The circuit itself would be rather simple, essentially given by the left part of the above-mentioned figure.
Anyway, a nice project but the expectations shouldn't be set very high...
On the other hand, a photodiode meter is very simple (one is described in Sam's FAQ which I have slightly modified and which works fine) and very sensitive and extremely linear at low intensities, but absolute measurements are next to impossible. Relative measurements are fine, for example determining reference/object beam ratios or optical densities.
However even these are not more accurate than say 10-20% because of dependence on the lighting, etc. That is, I was trying the measure the attenuation of some beam splitter, and one day the intensity ratio is consistently 55%, next day with more or less the same geometrical setup it is 60%, etc.
I don't think that one can do much better than that, but for hobby purposes it is anyway not that important.