I relate tinny to having a compressed response range (roll off on both lows and highs) without a full sound throughout (I feel that an adequate bass reproduction goes a long way in giving the sound depth and body)-- making the timbre of the upper mids-treble stand out and be extremely metallic sounding.
I think it can legitimately be used as a word to describe sound, it just needs to have a universally supported definition.
In reality you could just call tinny as a fancy word for thin-- which is pretty much what I described in my definition above. Tinny itself is apparently well known enough to get its own definition on my mac's little dictionary wiki:
tinny |ˈtinē|adjective ( -nier , -niest )having a displeasingly thin, metallic sound :tinny music played in the background.
Edited by TMRaven - 4/27/11 at 6:19pm