Searches for New Physics in Diphoton Events in proton anti-proton collisions at sqrt(s)=1.8TeV

We present a detailed description of a search for anomalous production of missing E_T ($\mett$), jets, leptons ($e, \mu, \tau$), b-quarks, or additional photons in events containing two isolated, central ($|\eta| 12$ GeV}. The results are consistent with standard model 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 $\mett$. We set limits using two specific SUSY scenarios for production of diphoton events with $\mett$.