The present work points out serious flaws in the definition of several commonly used CT diagnostics for TD-DFT calculations, which are not independent of representation so cannot truly be said to measure electron-hole separation or exciton size. Proper measures ought to be invariant with respect to rotations of the occupied MOs and (separately) the virtual MOs, which is automatically satisfied by true expectation values but not by incoherent averages over excitation amplitudes. Metrics that fail to respect orbital invariance can become unstable with respect to changes in basis set, even when those changes do not affect excitation energies or other expectation values. Furthermore, lack of orbital invariance introduces an arbitrary decision regarding which representation should be used to evaluate the metric in question. Different representations may afford dramatically different numerical values, leading to ambiguity in what is or is not classified as a CT excitation.