With the development of increasingly larger and more complex telescopes and instrumentation, site testing and characterization efforts also increase in both magnitude and complexity. This happens because the investment into larger observatories is higher and because new technologies, such as adaptive optics, require knowledge about parameters that did not matter previously, such as the vertical distribution of turbulence. We present examples of remaining questions which, to date, are not generally addressed by "standard" site characterization efforts, either because they are technically not (yet) feasible or because they are impractical. We center our observations around the experience gained during the Thirty Meter Telescope (TMT) site testing effort with an emphasis on turbulence measurements, but our findings are applicable in general to other current and future projects as well.