Is there a thing as "in sync" You could be off by 1 trillionth of a sec. a computer would never detect that?

Yes, there is such a thing as "in sync", but you have to be working at the quantum level. That's how a pulse laser works - all the atoms give off light sync'd together (but the laser has to be cooled down to almost absolute zero). But for most things larger than a few atoms, it is difficult or practically impossible to be exactly in sync.

For example, two different atomic clocks constructed and operated with state-of-art methods, will still differ at a rate of 1 trillionth of a second in about 12 minutes, that adds up to 1 second in 21 million years.

The best devices today can easily detect time difference of 1 trillionth of a second; in fact they can do 400 times better.

That's a trick question. For example, let's say two transmitters send out signals at exactly the same time. If you are closer to one transmitter than the other, you'll get the signal from the closer transmitter first so it will look to you like they aren't in sync. This is how GPS works.