If the question is at what scale a vector of change can be considered reliable given the 30m sampling. Well that partly depends on the data values - i.e. its a question of noise to signal.
If the amount of change is quite high, i.e. the reflectance values between two classes quite distinct, one would be happy with a finer scale of map.
As to the absolute minimum for Landsat, in reality each 30m pixel is really a representation of light gathered from a fuzzy circle on the ground around its center. The corners of the pixel are the radius of that circle. Beyond that point, reflected light is having more influence on neighbouring pixels. A bit of trig shows the radius to be about 42m. Thus there is an overlap of up to 12 meters each way for both axes. So any attempt to draw a vector along a line of change cannot be meaningful at less than a smallest object of 42m assuming that adjacent pixels received very different signals. The smallest scale is thus the smallest one can physically draw a map and still represent that size of object.
However, usually the signals are not that clear cut between individual pixels, the noise from the overlap is significant relative to the difference in spectral response. So the true smallest scale will be that at which the classification produces statistically distinct differences between landscape patches. Demanding that each class be statistically distinct from its neighbours aggregates similar pixels together. Once that is achieved, the smallest patch left defines the smallest scale which can be clearly seen.
I suspect what you really wanted was Ardit Sulce's answer which I also liked, but perhaps this was at least interesting!