By far the most common problem reported is random lockups when the machine is under heavy CPU load. Other sporadically reported problems include programs segfaulting, issues with the ATA66 controller, overheating and other random problems not specific to the BP6. The difference between the lockups and other problems is the consistency: while the reports of other problems (excluding the issues with the IDE controller) are probably about as common as they are with any other modern motherboard, the lockups are unique to the BP6 and appear to affect the majority of the owners.
For many (most?) people, their BP6 is perfectly stable as long as they're not running very CPU intensive tasks, such as the RC-5 client or Seti@Home. xscreensaver causes problems for others. People who have had problems report a wide range of mean times to failure. For some, their machine will crash in a matter of hours if running the aforementioned tasks. For others, they can go a week or more between crashes. Generally, 2 to 3 days seems to be the average time to crash a machine. Michael Rasmussen reported that they could crash their machine in under an hour by running several copies of Lucifer, a program designed to stress-test CPUs along with xscreensaver.
It's been suggested that using FPU intensive programs is a cause. It's possible this is a factor, or it could just be that CPU intensive programs tend to be FPU-centric. [ed: Anyone have any strong feelings about this either way?]