  The complete ensemble of Einstein Imaging Proportional Counter (IPC) X-ray
images has been re-processed and re-analyzed using a multi-aperture source
detection algorithm. A catalog of 772 new source candidates detected within the
central regions of the 1435 IPC fields comprising the Extended Medium
Sensitivity Survey (EMSS) has been compiled. By comparison, 478 EMSS sources
fall within the same area of sky. A randomly-selected subsample of 133 fields
was first examined. We found that most of these sources are either the
summation of two or more lower count rate point sources that fall within the
larger detection apertures or are single point sources, while \leq 2.3% of the
full catalog of sources are extrapolated to be actual distant (z > 0.14)
clusters whose extended X-ray structure kept them from being detected in the
EMSS despite having sufficient total flux.
  We then constructed other subsamples specifically selected to contain those
X-ray sources most likely to be clusters. Both a database search and an optical
imaging campaign have found several new distant clusters, setting a firm lower
limit on the number of new clusters in the entire catalog. We estimate that the
original EMSS cluster sample is 72-83% complete. We update the Henry et al.
1992 EMSS distant cluster sample with more recent information, and use the
redshifts and X-ray luminosities for these new EMSS clusters to compute a
revised X-ray Luminosity Function (XLF). The addition of these new high-z,
high-L_X clusters to the EMSS is sufficient to remove the requirement for
``negative'' evolution at high-L_X out to z~0.5. We conclude that the EMSS has
systematically missed clusters of low surface brightness.
