Mean time between failure(MTBF) is a measure of how reliable your system is.
The failure itself is open to interpretation. In your instance you could say a bit flip is a failure.
Fortunately the synchronizer would most likely correct itself after a few clock cycles.
When doing safety and reliability on hardware the quantity of components is a useful in getting a measure of MTBF.
Reading up on Mil-hdbk-217K could give you further insight into the world of reliability.
In general, the calculation of the MTBF takes into account aspects of physical failure of the component of the kind irreversible (damage), but it is not entirely clear if you are considering just flaws in operation, as wesleytaylor mentioned.
"Failure" in terms of metstability means a detectable occurrence of a metastable event, can be e.g. detected as a FF output voltage not reaching a defined high or low level at sampling time. At page 5 of the appended Altera application note, a test circuit to measure metastability is suggested.