I was curious to see how accurate the displayed ephemeris are (http://voyager.jpl.nasa.gov/Scripts/distance.js) given that they are known very precisely indeed.

For instance, ranges to Saturn are known to better than 1km, and Mars to better than 10m (http://tmo.jpl.nasa.gov/progress_report/42-178/178C.pdf, e.g., fig. 1 for Mars), and we don't even get to take direct measurements of those bodies as we can for the Voyagers.

Alas, the js seems to simply be interpolating between two known values, at a spacing of 1 year (86400s):

   var epoch_0 = 1373990400;
   var epoch_1 = 1374076800;
    [...]
   var dist_0_v1 = 17396281625.1305;
   var dist_1_v1 = 17395807835.8111;
   current_dist_km_v1 = ( ( ( current_time - epoch_0 ) / ( epoch_1 - epoch_0 ) ) * ( dist_1_v1 - dist_0_v1 ) ) + dist_0_v1;

I'm not sure how to square this linear progression over a 1-year span with the comment in the OP that "Because Earth moves around the sun faster than Voyager 1 is traveling from Earth, the distance between Earth and the spacecraft actually decreases at certain times of the year."