It appears that this is not the first time where humanity had to face
a millennium problem.  According to recently unearthed records, the
last one was substantially more devastating:

A set of tablets and papyri scrolls discovered by archeologists in the
Kilios caves on the island of Chronia tell about the troubles caused
by the change of the clocks and the calendars at the beginning of the
Christian Era (CE), when it was decided to stop counting backwards
(100 BCE, 50 BCE..etc) and switch to an ascending count (and drop the
B for Octate-Economy).

Governors, kings and emperors decreed that all palaces, temples, roads
and public buildings built for the state must bear the Y0K [1] Compliance
Certificate issued by the RSI (Roman Standards Institute).  The
abacuses used to whip the horses on the different local and imported
chariots had to be certified or replaced.

Thousands of retired carvers have been rehired to erase all the
engravings on the sundials and replace them with clock-wise numbers.
Most of these carvers were trained during the last Calendar Crisis:
when Julius Caesar stole a day from February to add it to his own
month (He was killed a couple of weeks after the senators discovered
the missing day in February.  Augustus stole another day a few years
later, but people then realized that this shortens winter and
increases summer, so they deified Julius and Augustus).

The last Egyptian carver had already been mummified, so no one could
fix the obelisks or the pyramids.  Their owner could not replace them
in time, so he turned into a sphinx.  (He was not the only victim of
Y0K, hundreds of tourists were caught off guard while vacationing in
Easter Island).  Others who were petrified by the experience were used
by the Mayans as calendar pages.

Major changes had also to be done to all the sand-based and
water-based clocks.  The mechanisms had to be modified to fall
downwards instead of jumping upwards.  A Greek researcher attached to
the Syrakico HelioPyryniko Kentro (The Sicilian Laser Institute for Ship
Burning), enacted a law that pulled sand and water downwards.  The law
stated that 'whatever goes up should come down' (He called it Eureka because
he couldn't spell Buoyancy.  A British Apple-Eater, who could not spell
either, renamed it Gravity).

The Y0K problems were not limited to the Mediterranean, some were
reported also on the British isles:  The Celts had just borrowed England
from the Picts.  With the loan came two time-tracking machines:
Stonehenge and Woodhenge (a small wooden prototype of the stoned one).
To resolve the Y0K problem, the Celts decided to re-order the henges,
starting with the wooden prototype.  The Druids hired a group of Scots
to do the job.  But after removing the wooden posts, the Scots started
tossing them.  They called that the HighLands games:  throw the log
high so that it lands on the Druids who didn't know yet about the Eureka
law.  By the time these games were over, all the wooden post were
mixed up and all the Druids flatened (except for Merlin who escaped on
a camel lot).  The Scots' Captain, McCurling, proposed to fix
Stonehenge. But Hadrian send them golfing on the north side of his
wall.  Stonehenge was never fixed but is still used by stoned hippies
and people who drive on the wrong (right) side of the road.

Besides all these technical problems, a number of legal and financial
disagreements exploded.  The most notorious is the question on whether
there was a Year 0 (zero) CE:

Financial institutions and teen-agers insisted that there was.  Banks
charged interests for Year 0 CE on all loans incurred BCE.  Teens born
BCE claimed that they are one year older and can therefore drink and
drive their father's chariots (and set them on fire).  Both groups
insisted that there was also a Year 0 BCE.

Mortgage holders and parents (and ladies born BCE) insisted that zero
was not invented yet, therefore Year 0 CE never existed.  The Phoenician
bankers dispatched the Arabian knights to the Hindus Valley to discover
nothing (zero). The Year-0 debate is still rageing on some electronic
discussion groups.