What is the most overlooked consideration?

I think one of the most overlooked considerations is long-term reliability. Everyone gets caught up in specs and brand reputation, but hardly anyone asks if it will still work perfectly five or ten years from now. I’ve had gear that sounded great at first but developed issues within a couple of years. It’s easy to get swept up by new features, but I’d rather have something that lasts.

The crossover in the loudspeaker. I think I'll start a thread on that subject.

The equipment’s grip on the reproduction of the emotion of the composition and performance.  +1 for @ghdprentice term - musicality and his recommendation to not focus on the usual audiophile criteria.   The prerequisite is to experience the emotion of live acoustic and amplified musical performances.  Then you can evaluate the equipment’s grip on the music compared to this benchmark.  I agree it is unrealistic to expect to bring the music hall to your listening room.  However, the equipment should, at a minimum, bring memories of the emotional experience of a  live performance, and should evoke similar emotions to the reproduction of music in your home.  Yes, it is a  personally subjective criterion.   However, if the equipment is melodious to you, you will be engulfed in the emotional experience that the recorded composition and performance evokes.  

Not to hijack since it was mentioned twice I would pose this to the repliers commenting on the "musicality"of a component..How the H do you judge a components musicality if you are considering it for purchase & don’t yet own it?
ONLY the "usual"audiophile criteria can be used at this point of the process!

This is by no means the primary consideration, but as a retired person on a comfortable but fixed income, one of the things i always consider is whether a component is desirable by others and can I purchase it for a good price. Can it be flipped quickly, without losing money or at a slight profit.