If I remember correctly, standard C14 dating has
about a 10% standard deviation in which the actual
date has a 95% chance of being within 1 SD and a
99% chance of being within 2 SD's. The nearer to
the present, the less apparent accuracy. If a 10%
C14 date is 1650±50, it's less reliable than
pottery dating. However, the newish variant of C14
called Accelerator Mass Spectrometer dating gets
down to about 1%, again if memory serves, such
that the date would then be 1650±5.

I think it was 1955 that the hydrogen bomb
exploded, polluting the atmosphere with lots of
excess C14 so that's when the so-called modern era
begins or B.P.

C14 has been around the longest and has the most
bugs worked out of any of the absolute dating
systems. The only dating system which works any
better would appear to be dendrochronology and
then only in some circumstances and then of course
when there's wood surviving.