A problem with DNA is that it will degrade. DNA degradation means that the stuff just breaks in peaces. You will need a high redundancy to recover the original information by de nove assembly of the pieces.

In addition, nature has provided us with various tools for reading the DNA information (enzymes), and replicating existing pieces of DNA, but lacks a mechanism for writing new DNA. Chemistry has come up with answers in this respect, but creation of large accurate molecules is still a challenge. It is of-course advised to store the information in small pieces, because then it is less prone to degradation as well.

I am sure technical improvements will resolve these problems, so I foresee that DNA data storage will become a big thing in the future!