That you can store large amounts of data in DNA, and recover it, should be surprising to nobody. It should also be surprising that no matter how well it works, it won't ever become a viable product.
Yes, mutations occur. Randomly. This means that if you sequence a set of DNA molecules the consensus sequence can still render the proper data string despite flaws in each individual copy.
In the context of generating organisms like this, so long as your stored information is not in a loci that could be mutated to regulate proliferation in a positive way, mutations in your storage string wouldn't propagate in a consensus manner (in some organisms, it's hard to make them grow faster. E. coli for instance have already been optimized to divide pretty darn quickly by evolution).
The same is true for populations of DNA molecules rather than organisms (are any organisms much more than DNA storage and maintenance machines :-D?). Random mutations in one molecule in a tube would be different for each neighboring molecule, but the consensus sequence is still valid.
This all makes perfect intuitive sense when you recognize that even some DNA sequences with no positive effect on growth are fairly well conserved on evolutionary timescales. https://www.wikiwand.com/en/Long_terminal_repeat https://www.wikiwand.com/en/Alu_element
Also, DNA kept in a dry, cold environment has an effectively infinite lifespan. Now, the interesting question becomes "what fraction of the the lifespan of the universe can I maintain my data with arbitrary accuracy?"
Next, existing technologies are more mature. They provide off-the-shelf products that integrate into a large ecosystem. So, DNA would have to provide some niche value that hard drives or flash drives don't.
Finally, with durable storage mechanisms, you don't really know how well they work until you deploy many instances of the mechanism for their lifetime; for DNA storage, that would be billions of cells (or more likely, passive storage containers) for decades or more.
So, I'll go with tapes, hard and flash drives and everybody else will too. MSFT made some claims about rolling out DNA_based storage in the decade-future, but they're blowing smoke.
1: http://onlinelibrary.wiley.com/doi/10.1002/anie.201411378/ab...
Showing you can store a tiny amount of data and then claiming you have a density higher than hard drives isn't just poor marketing, it's outright lying.
To show durability, you need to actually test things for the planned lifespan, or use intelligent mechanisms to test in a shorter lifespan. Then you can claim durability.