Just signed up to chime in on this.
PID doesn't seem to do anything to actually trip any flags. First, I went and looked through my gen 3/4 mons to find six that had invalid PIDs - I put them all on a team, and I was able to go on battle spot with them. Then, I genned a shiny Emerald Mew, with an invalid PID of course, and I managed to trade it to strangers online. I've tested this again and again since then, and the only problem I ever had was with a Huntail not having been traded, I believe.
From what I've seen, you can just ignore PIDs being invalid altogether.
