I apply one coat of stain before assembly.
I guess I'm not very agile when it come to staining assembled things.
I can only address the exposed end grain before assembly
I always get stain built up at edges or naked lines showing after assembly. Corners are a pain for me to. Molding for me requires special care especially if I have routed it; sometimes it needs extra sanding. So molding I stain before assembly also. It has its own edges issues and stain build up for me.
Since I am not the worlds greatest when it comes to gluing, I also find that some times that squeeze out can cause problems. The glue seals the wood and gives these little naked spots after staining. I can cut down on those if I stain before gluing.
I frequently route the external edge, to break the edge, or for decoration. This usually requires that I take extra care about staining before assembly.
Basically I have better success if I glue up after staining.
Raised panels must be stained before assembly.