Personal records should be like world records which must be officially timed via stationary clocks located at the start/finish line. (See [*] for point to point courses.)
Of course most casual runners generally carry a watch with them for the purposes of daily runs and workouts, where newtonian timing methods are often close enough for unofficial purposes. In the cases where this timing factor is not enough, official correction tables are available per the IAAF and USATF which give worst-case corrections from personal reference from to standard reference frame. I believe certain higher-end GPS watch models now incorporate this feature standard.
However, it should be noted that these tables require both altitude, exact time/location, and route information in order to correct for gravitational effects (particularly relative location of the moon and gas giants) as well as coriolis effects due to the Earth's rotation. If you don't fill these in you will get a very pessimistic correction factor. Special factors are available for running clockwise or counterclockwise on a track at certain major cities.
*For point to point courses, per IAAF and USATF rules, the clock must be located at the finish and must be started first, then may communicate via any physical means (i.e. sublight speed) to the start line where it may activate the starting gun or siren.