One thing I think is important, is to know the operation limits of your opamp, like: output voltage saturation values, INPUT voltage saturation values, max and min Input and output currents, min input voltages, etc. Most of these specifications can be found in opamps' datasheets, but there are cases where SOME of these specs are not found, so there's where you need to try to understand the internal workings of your device.
I also think that if you have the time and pacience you should try to undestand how things work very down below, cause you never know when you're going to need that extra knowledge to solve other problems.