Nice work, friedo.
On the physics…
The omega minus (or [symbol]W[/symbol][sup]-[/sup]) was discovered in 1964 at Brookhaven National Laboratory. This L&O episode took place in 1994, so that would make the victim 56 years old. Seems reasonable. The actual experimental group had 33 members, none of whom (of course) were named Manning. (Journal article for the [symbol]W[/symbol][sup]-[/sup] discovery: Physical Review Letters 12, 204–206.)
The proton decay detection method outlined is reasonable. That is, a vat of liquid viewed by light-sensitive photomultiplier tubes is a common setup, and the scale of the active detector volume (i.e., the size of a very large room) is reasonable.
Both proton decay modes mentioned are actually searched for. The one Weiss poo-poos is favored by many grand unified theories, partly because the daughter particles are the lightest charged lepton [electron] and hadron [pion] possible, a situation which has certain advantages. This mode is also relatively easy to search for because the two-particle final state (as opposed to three or more particles) means that the electron has a specific energy and the pion has a specific energy. You need only look for those two particles with those exact energies, so the expected rate of “fake” signals is low.
The other decay mode (p–>e[symbol]n[/symbol][symbol]n[/symbol]) is also viable and searched for by experimentalists, although detection is more difficult. The outgoing electron’s energy can cover a wide range (rather than always being the same every time), and the outgoing neutrinos go completely undetected. Thus, in the lingo, one would say that the “signature” of this decay is more easily mimicked by other processes, making it a bit harder to study (but not insurmountably so).
It is further possible that Manning had designed his analysis software to look solely for the e[symbol]p[/symbol] channel and not the e[symbol]n[/symbol][symbol]n[/symbol] channel. This would have been overt, though. He would have presented his results as such (“A Search for Proton Decay via p–>e[symbol]p[/symbol]”, or whatever) and everyone would already realize that he didn’t look for other decay modes.
Regarding “we can synthesize three of the basic forces of the universe”… Weiss is noting that the observation of proton decay would be a boon for grand unified theories, which (sometimes) predict proton decay and which indeed are attempts to integrate our descriptions of the electromagnetic, strong, and weak forces into one well-behaved package (that is, “synthesize three of the basic forces of the universe”).
Regarding “we would be on the verge of reading the mind of God”… Erm, maybe.
Anyway, they very clearly had a particle physicist on hand, as these bits of dialogue are surprisingly realistic in content (if overly dramatized in tone).