The biggest flaw with the sound of the LCD-2 is something I never noticed until I had them in my home. These headphones do not know what dynamics are. It's as if, hidden in the cups, there is a normalization circuit that puts everything on the same volume level. Obviously this is a bit of an exagerration, but not far from true. When there are multiple sound sources playing at the same time, they are all roughly the same volume. This makes listening to solo concertos challenging to say the least.
I feel somehow validated that you've mentioned this about the LCD-2 as well and wanted to quote it to bring more attention to it. That was one of the things that bothered me most about both the LCD-2 and LCD-3 when I tried to listen to classical music on them. I've actually found that true musical dynamics are lost on most headphones and only a very few headphones I've heard accurately portray "quiet" and "loud".