In addition to factors mentioned in the FAQ (excellent, btw) I'd add in time of day, external pressures (job or family related), length/type of warmup, recent training, temperature.
I use HR as a long term indicator - as I get fitter my resting HR drops, my speed for a given HR increases etc, - over say 6 months.
But week to week, month to month my performance on a standard work load is much more precise and valuable.
From the excellent FAQ
Three variables to control in any training program are intensity, duration, and frequency; of these, the latter two are easy to quantify objectively – duration is measured in hours, and frequency in sessions per week (the product of the two is volume). Intensity, on the other hand, has traditionally been measured by perceived exertion (PE) and/or heart rate (HR).
HR is reliable enough at lower (i.e., aerobic-only) intensities, but for more race-specific (i.e., shorter but more intense) training, it becomes a much less effective proxy for intensity.
Since most of the training mentioned here is aerobic it seem HR
IS reliable I don't have a problem with Power meters if I was still racing I would have one but it is just a tool and for exactly the reasons you mention above work, time, family etc I think a hrm will for most people give them exactly the same training benefits. Training is about adapting to higher loads, a hrm gives a good indication how your body is coping with the overall demand so as you approach your volume limit and the risk of overtraining, with the setbacks that causes, a hrm quickly lets you see that you can't get your hr into the zone, with a powermeter only I think the temptation would be to try and maintain the load dictated for that session by the powermeter.