Number of errors that can be detected with a single-bit even parity code word system?
I'm not sure exactly what you're asking.  If you fail a parity check, you are assured that there is at least one bit of the 8 in error (it may be the parity bit).  There may be 3, but you have no way of distinguishing the two results.  Further, if you have an even number of errors, they will result in no detected error at all.

No matter what, you have no indication which bit is in error, so parity is useless for any error correction.

Parity is generally used in systems which are reliable enough that the probability of having more than one error in N bits (N=8 in this example) is considered negligible.