The comments from Phil Sweet and sumelic match my intuitive sense of the words and the definitions in my dictionary (Summary: impair = to weaken; impede = to obstruct).
It's a clean distinction in theory. A car that is blocked by a boulder in the road is clearly impeded and not impaired. But in practice, I think it can be muddy, esp. as you get more metaphorical. If I have Parkinson's disease and can't go up stairs, that could be seen as a weakness, but the disease itself can also be seen as an obstacle. If I have to fight with one hand tied behind my back, am I impaired or impeded? I would say both. I think a "weakness" can be seen as a sub-type of "obstacle," so you may need to choose one word or the other based on whether you wish to emphasize the weakness of the person trying to do something, or the strength of the thing in her way.
The example is interesting, though. It seems metaphorical, and I can see either sense: A procedure (law, rule, etc) may "weaken" me by not allowing me to use certain capabilities. Or the procedure itself may be seen as an obstacle standing in my way.
This is very subjunctive, but I think "procedural impediments" is less likely to be misunderstood. "Procedural impairments" may be taken to mean bad wording that make the procedure itself less effective; e.g., loopholes.
Either way, to answer the question, I don't see the difference as related to the abstract/concrete distinction.