We present a detailed description of a search for anomalous
production of missing E_T (/E_T), jets, leptons (e, mu, tau), b-quarks, or
additional photons in events containing two isolated, central (|\eta| < 1.0)
photons with E_T > 12 GeV.  The results are consistent with standard
expectations, with the possible exception of one event that has in addition to
the two photons a central electron, a high-E_T electromagnetic cluster, and
large missing E_T.  We set limits using two specific SUSY scenarios for
production of diphoton events with missing E_T.