I've had my Arduino for a while now, but I can't remember ever seeing this happen: when I'm powering my Arduino with a wall wart (12V, 1.2 A) both the Tx and Rx LEDs say solid on, even if there is no serial communication. When there IS serial communication they'll flicker a bit. Despite this, everything works fine (I'm using an Xbee + Shield to transmit serial data).
I just wanted to check and make sure this didn't mean something unusual/unsafe was happening? I apologize if this has been answered before, I was unable to find it.