From what i'm seeing on my card (in win7 /w 9.10) the issue is that in multi-monitor mode the 5850 appears to default to a 400MHz/1GHZ (core/mem) idle speed.

However when you are overclocking the card (even by 1MHz), it uses the 157/300MHz idle speeds instead. This can likely be fixed by a modified bios with a different idle clock for the OC'd state; (there are two 157/300 entrys in the 5850 bios) or possibly ATI might fix it in a driver update.

Although any flickering should go away in games as the clockspeed goes up, your BF2/2142 poly problems are likely a separate issue.