12 Noon, is that 12 pm or 12 am?

You have indeed answered you own question : a.m. and p.m. are nonsensical when used with "noon", and should not be used.

But does it really matter? There are millions of ignorant people who are always misunderstanding and misusing concepts and language of technology, and they will always be with us (and journalists and broadcasters are some of the worst offenders, in my opinion, and only serve to increase confusion).

a.m. and p.m. are there to remove confusion when dealing with the rest of the day, when confusion may arise because we use the 12-hour clock twice over. I don't think anyone is really going to confuse noon with midnight, are they ? (Mind you, some people can be really .... )

12:00 is neither am or pm. 12:00 is noon or midnight. One minute before noon is 11:59 am. One minute after noon is 12:01 pm.

PM

Actually a better translation for ante meridiem(AM) would be "before mid-day" and post meridiem(PM) would be after mid-day, therefore 12 noon being 12PM makes sense because a day starts at midnight and at noon it passes the middle of the day.

Then let's use the digital:
12 midnight = 00:00:00
12 noon = 12:00:00

Such that:
12 AM = 00:00:00
03 AM = 03:00:00
06 AM = 06:00:00
09 AM = 09:00:00
12 PM = 12:00:00
03 PM = 15:00:00
06 PM = 18:00:00
09 PM = 21:00:00

AM stands for ante meridiem (meaning before noon) and PM stands for post meridiem (meaning after noon)

just thought id give more of a "why" answer :)

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12:00 exactly(with no seconds) in neither AM or PM. 12:00 noon and 1 second is PM

Actually, "ante meridiem" and "post meridiem." are no longer the definitions of 'am' and 'pm'. The terms 'am' and 'pm' have acquired a meaning of their own with 12 am meaning midnight and 12 pm midday. It is completely arbitrary, the terms might have gone the other way, but since there is almost universal agreement it is a useful convention.

A high proportion of words have changed their meaning since they began. The language would be far poorer if anyone ever managed to stop this process.

"12 am" and "12 pm" was never defined in the first place. It was made up by the common ("couldn't care less") people trying to make things easier.

Institutions that specialize in defining and measuring time had always used the 24 hour format or simply called them respectively (12) midnight and (12) noon.

Astronomical noon seldom occurs at at 12 noon. It can vary by up to 20 minutes before or after the meridian. Noon is when the sun is at its highest point in the sky, when it crosses the meridan.

For normal people 12 noon is PM. But if you work nightshift like myself, noon is AM.