But what's so special about November 1858?
Nothing, other than that was when JD 2400000 occurred. Look at all of the zeros! The next time we'll see that many zeros will be noon on August 31, 2132.
It is not possible to achieve microsecond level accuracy if one expresses time as a double precision Julian Date. (It will be possible to maintain millisecond level accuracy using a Julian Date for another 100000 years.) Until recently (August 3, 2001), microsecond level precision was possible using a Modified Julian Date.
An alternative is to use the IAU SOFA convention, in which one specifies time as a Julian date using a pair of doubles that conceptually add to the time in question. Typically, the first of the pair is some value that can be represented exactly (e.g., 2460007.5) and the second is an offset from that base time. The recommended practice is to use the Julian date of the J2000 epoch (2451545.0, or noon January 1, 2000) as the first of the two doubles. With this approach, astronomers can easily achieve microsecond level precision until September 18, 2142.