I unlocked the 4th core on my Phenom II X3 720 BE but it's unstable...

There's a reason ATI/AMD disabled that 4th core and sold that processor as an X3 720 BE instead of a Quad Core. Finding a "stable" 4th core on the 720 is like winning a small local lottery.

You could try overvolting the whole CPU in hopes that more voltage would make that 4th core stable, but then you're looking at extra heat and other potential issues.

The only way to 100% run that CPU stable is to disable that 4th core again.

Yes - but sometimes the reason is because demand for the 720 chip exceeds the supply of 1 bad core chips they have on hand so they take perfectly good chips and disable the core - THis is why there are some chips that are perfectly stable with the fourth core unlocked ( I happen to have gotten one that has been running for about a month 24\7 with the 4th core unlocked and a small OC to 3.0 GHz. so they are out there !) - Seeing that it was bought in the begining of DEC. just before the start of the christmas shopping season they probably had to make some 720's with perfectly good fourth cores to fill the demand they would be getting during the holiday and I was lucky enough to get one.

That being said though you are correct that in this case it would seem there actually is some defect in the chip so best thing to do would be turn the 4th core back off and use the chip as a X3 like he bought.

"Hyper Transport sync flood error" has nothing to do with the core being unstable. That is a known issue with MSI and Asus boards and you should be able to work your way around it with the latest Bios update. Update the Bios and try again...

When not enough volts are being provided to the CPU it will reboot at any time (Especially during heavy to max loads) with either a black screen or verticle lines right before rebooting. While posting you see this messege.

"hypertransport sync flood error has occured. Press F1 to resume"

So there are a number of Scenarios that may cause this BUT they ALL lead back to the main reason. Not enough power to the CPU at the time that the heavy load produces failure.

1. To high of an OC without the ample amount of CPU volts.
2. Plain, not enough CPU Volts at any speed.
3. Possible Bad power supply.
4. Motherboard with very high amount of VDroop which ultimately leads back to "Not Enough CPU Volts".

With the most recent Bios and the correct amount of CPU voltage you should not see that error message again...

I know, but MSI tech support insists that it's a fault with the core. They refuse to help me.  

Oh well, thanks for the help.

So you arent going to try to update the BOIS to see if it fixes it? Cus i unlocked my 720 BE and man is it ever nice.

tech support do not over clock, why? they want you to sink money on their top end product for no reason, and even then they would likely to not help you.