  Currently there are two significantly different observational determinations
of the primordial helium abundance, and, if only statistical errors in He4
abundance determinations are considered, the discrepancies between the
observational determinations and the value favored by the WMAP results are
significant. Here we examine in detail some likely sources of systematic
uncertainties which may resolve the differences between the two determinations.
We conclude that the observational determination of the primordial helium
abundance is completely limited by systematic errors and that these systematic
errors have not been fully accounted for in any published observational
determination of the primordial helium abundance. In principle, the observed
metal-poor HII region spectra should be analyzed in a non-parametric way, such
that the HII region physical conditions and the helium abundance are derived
solely from the relative flux ratios of the helium and hydrogen emission lines.
In practice, there are very few HII region spectra with the quality that allow
this, so that most analyses depend on assumed ranges or relationships between
physical parameters, resulting in parametric solutions with underestimated
error bars. A representative result of our analysis yields Y_p = 0.249 \pm
0.009. However, given that most of the spectra analyzed to date do not
significantly constrain the primordial helium abundance, we argue in favor a
range of allowed values of 0.232 le Y_p le 0.258. [abstract abridged]
