Sensitivity of calculated orbital elements to observational errors
Kepler used data from catalogs made by Tycho Brahe which had a varying level of precision and accuracy down to about 0.5 arcminutes for a measurement. However, since Kepler thought all systems should operate in the same way, he could use a larger sample verify his laws. Once you know what the relation should be, you can then map the observations to what you would expect. For an individual case, the precision of measuring orbital parameters depeneds on how much of the orbit you have actually observed.