Transient lunar phenomena (TLPs) have been reported for centuries, but their nature is largely unsettled and remains controversial. In this Paper I the database of TLP reports is subjected to a discriminating statistical filter robust against sites of spurious reports, and produces a restricted sample that may be largely reliable, and is highly correlated geographically with event catalogs from Apollo and Lunar Prospector alpha-particle spectrometers for episodic ²²²Rn gas releases. Both this robust TLP sample and even the larger, unfiltered sample are highly correlated with the boundary between mare and highlands, as are both deep and shallow moonquakes, as well as ²¹⁰Po, a long-lived product of ²²²Rn decay and another tracer of outgassing. This offers another significant correlation relating TLPs and outgassing, and may tie some of this activity to sagging mare basalt plains (perhaps mascons). Additionally, low-level but likely significant TLP activity is connected to recent, major impact craters (while moonquakes are not), which may indicate the effects of impact fracturing, or perhaps avalanches, allowing release of gas. Most TLP (and ²²²Rn) activity, however, is confined to one area likely causing major, recent volcanic effusion, and plausibly connected to the deep lunar interior. Our accompanying paper (Crotts & Hummels) treats likely theoretical implications, plus practical methodologies for remote and in situ TLP and lunar outgassing observations. With the coming fleet of robotic lunar spacecraft, followed by human exploration, the study of TLPs and outgassing is both promising and imperiled. We anticipate a greater burden of anthropogenic lunar gas than ever produced, perhaps outstripping the natural atmosphere itself, but also unprecedented opportunities to study lunar outgassing and its sources if these can be examined promptly, in their pristine state.