When it is 24 minutes past the hour in one country, it is guaranteed
to also be 24 minutes past the hour in every other country.

At one time in the past, this must not have been the case. The exact
time must have varied between countries.

How, why and when did this international synchronisation occur? Did it
happen overnight or was it a gradual process over time? Were there
issues when a country "lost" minutes?

mhearn-ga,

It's actually not the case that when it's 24 past the hour in one
country, it is in all countries.

There are a surprising number of places in the world with
idiosyncratic time zones that are offset from the major time zones,
generally by 15 minutes or 30 minutes.

The reason for the variability is that each jurisdication around the
world gets to make its own choice about how to set the local time. 
This includes choosing whether to rely (or not) on the global time
zone system of 24 hourly segments, whether to adopt (or not) daylight
savings, and whether to divide (or not) large expanses into multiple
time zones.

This results in numerous oddities.  

For instance, there are many more than 24 time zones in the world...by
some counts as many as 39, plus a few areas without an officialy
recognized time.

Crossing from some zones to an adjacent zone can result in a time
difference as large as three and a half hours!

There are places in the world where more than two time zones meet at one spot.

And there are huge countries -- China, for instance, -- with only a
single time zone.


Given the fact that countries and other jurisdictions get to choose
how, when and why to set their clocks as they do, there isn't a single
point in time when the world's clocks suddenly became synchronized. 
Nor is there even what one could call a smooth historical transition.

There is a very good overview and historical summary of the global
time zone system (and its numerous exceptions) at the Wikipedia online
encyclopedia:


http://en.wikipedia.org/wiki/Time_zone
Time Zone


The site includes a nice map of the world's time zones:


http://en.wikipedia.org/wiki/Image:Timezones_optimized.png


and if you want a good look at it, you should download the beautiful,
high-resolution verion here:


http://upload.wikimedia.org/wikipedia/commons/3/3d/Timezones_optimized.png
 


I think this should give you a terrific overview, and should provide
all the information you're after.

However, if there's anything else you need, just let me know by
posting a Request for Clarification, and I'm at your service.

Cheers,

pafalafa-ga


search strategy -- Google serch on [ time zones ]

Pafalafa-ga is absolutely right. When its for example, 24 mins past in
NZ, it is definitely NOT 24 minutes past in India. I would like to
know where mhearn-ga got the idea.

Mhearn probably got the idea because he/she has always traveled in
time zones that are off only by hours and not minutes. It's easy to
see how someone could have that misconception. I myself was surprised
that it was not the case. Not everyone goes to India :)

Quite so, Keystroke.  
I understand that Nepal set a unique time zone for itself to emphasize
its separation from India, which would like to incorporate Nepal.
That type of political thinking could also explain the 1/2 hour time
difference between Pakistan and India.