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2. Need for the Moon

Certain observations are feasible only from the Moon.

2.1. Stable platform (vibration control)

The techniques for finding life on extrasolar planets require extraordinary stability. This stability level may be feasible only on the Moon due to difficulty in formation flying and vibration control in free space.
For the Terrestrial Planet Finder mission, it is almost impractical to build an interferometer in free space with a baseline longer than a few 100 m.
Lunar seismicity will have a very limited effect on the telescope because of the magnetic bearing.
Stability requirements for studying extra-solar planets with a coronagraph or nulling interferometer is much stricter than for any Earth-based observatory. For the coronagraph, we'd probably want on the order of 1 milli-arcsec pointing stability. Such a high stability requirement will demand that the telescope wait about 2 hours every time it repositions.4 For the nulling inteferometer, we'd probably want a beam path-length error below 1000th of a wavelength (10s of nm or lower).
Mode: below 10 Hz.

2.2. Cooling (sensitivity)

To stay sky-limited at ~20 microns, the telescope needs to be at least ~30K. In space, passive cooling to 30K is possible, but with huge multi-layer sun shields (which degrades over time with contamination by propellants and damages by meteoroids). Active cooling will be necessary anyways (for detectors), and a main reason we need the lunar surface is to control the vibration to the very high standard required for coronagraph / nulling interferometry.

2.3. Thermal stability (temperature control)

These techniques also require not only low temperature but also very stable thermal condition. Permanently dark floors of polar craters are probably the most thermally stable locations. In free space, temperature on the mirror varies depending on its orientation with respect to the sun shield.

2.4. Lower risk

Construction is much less risky on a solid platform with gravity than in free space where everything needs to be kept track of (e.g. by tethering). Accessibility from a nearby lunar base allows service / upgrades for never-ending contribution to astronomy