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And then, we should add the "length" of our mitochondrial DNA. Although it is much smaller than nuclear DNA (16.000 base pairs), every cell has between 100 and 10.000 copies of this mtDNA.
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>Most amazingly it would not be a light-year of random DNA sequence, but ten thousand trillion identical copies of your DNA, faithfully replicated by your cells.

Cell reproduction is a pretty imperfect.

Is pretty damn perfect for a chemical process. Each replication of the genome introduces only one error on average and given that the majority of the genome is junk DNA (not just non-coding, but actual junk), the single error is roughly analogous to a speck in the margin of a photocopied page.
Is it, though? I thought that the 'junk' DNA thing was a myth.
There has been renewed interest in finding out what non-coding DNA (aka 'junk' DNA) actually does. Some prominent theories are that some kinds of non-coding DNA are epigenetic controls, but there isn't a complete set of theories yet. There ARE transposable elements, sequences of DNA that can essentially move around in your genome at will, and cause problems by doing so: imagine getting a transport protein sequence in a stem cell cut in half. Even then, these are kind of like DNA parasites, not junk.
Sorry, I'm going to nit pick, but non-coding and "junk" aren't the same thing:

Non-coding just refers to not being translated to protein, and we know (as you list, more for the benefit of others) that there are many non-coding functional elements.

Junk DNA is non-conserved DNA (e.g. shows only neutral selection). And if it's not being selected for or against, then it probably doesn't have much effect either way.

I think people get emotive over the term 'junk'. It was always just a phrase rather than a technical description. We know that ~80%, maybe a little more, of the genome does not show conservation. If the function was important to the survival of the organism it have been selected for and thus evolutionarily conserved - hence the 85% "junk" figure. This does not mean that it isn't entirely biochemically inactive, or that there are some longer range periodicities in the sequence that are not elucidated. And as another commenter has noted, about half of the genome is composed of remnants of the Alu element, which jump about occasionally, but mostly degrade into total inactivity (sometimes being reactivated by recombining broken parts together).

What has gained a lot of attention was the massive ENCODE project, which sought to provide a detailed atlas of biochemical function in the human genome. The headline figure from there has been that 80% of the human genome has some function. There's a lot of controversy (understatement hat on) on the basic experimentation done for ENCODE, the structure of the project, the usefulness of the data produced and how they define biological activity.

The debate possibly got a bit out of control - the most sarcastic peer reviewed article I have ever read stirred the pot a bit (for more info: http://www.scilogs.com/next_regeneration/the-encode-controve...). I think most biologists (warning, personal opinion) would still hold that 80% of the genome is not meaningfully biologically functional.

From all I know DNA replication has a very low error rate. I’m not a biologist, so I lack the expertise to accurately judge papers about this topic, but the one I found (through looking the topic up on Wikipedia) suggests a very low error rate:

“In total, these three discrimination steps result in an in vivo mutation rate estimated to be […] less than one error for every billion (or more) bases pairs copied […]” http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3639319/

Your diploid genome is roughly six billion base pairs. That means six errors per duplication. But there will also be other errors introduced by DNA damage from other sources, and processes which have evolved to modify your genome (for example, V(D)J recombination).
All the humans who have ever lived (~107 billion) created DNA just a bit longer than the diameter of the observable universe (93 billion light years).
How do you define when Humans started to live, though ? Evolution is not a black and white process, we did not suddenly become humans and stopped being apes. It was probably very progressive and gradual.
At this scale, a factor of magnitude or two is of little consequence, and odds are, you can get general buy-in within a "factor of magnitude or two" of the number of humans to live from the vast bulk of people who might have sensible opinions.
In this case, it's actually very easy to get a good estimate: 10 billion is too low, 1 trillion seems a little high, 10 trillion is definitely too high; 100 billion is, as such, really the only good estimate.
I was wondering about what "two copies" meant. Chromosome pairs aren't copied from each other, but surely the author didn't mean to separate the DNA strand into its mirrored halfs, that must surely not be stable whatever you do.

The first reference given doesn't open without cookies enabled, so I looked it up on wikipedia instead [1]. The 3 billion number is the sum of the number of base pairs of all of the different chromosomes; i.e. the size of the genome data set that's (roughly) identical across all humans. So yes, one cell then instead has the sum of the number of base pairs of chromosomes 1..22 times two, plus the size of X * 2 or X + Y, which is approximately 2 * 3 billion. Thus the calculation is correct.

[1] https://en.wikipedia.org/wiki/Human_genome