DNA has the same limitation that many serial protocols have: if you repeat the same base pairs (e.g. "AAAAAAAAAAAAAAAAAAAAAA") you will have trouble w/ the DNA not spiraling correctly. Some sequences of 2-6 repeated base pairs seem to "deliberately" cause variant behavior in DNA and RNA, see

https://en.wikipedia.org/wiki/Repeated_sequence_(DNA)

Many real wire protocols have mechanisms to prevent repeated sequences entirely

https://en.wikipedia.org/wiki/8b/10b_encoding

DNA coding for real proteins is unlikely to be too terribly repetitive but I image a long α helix could have a repetitive amino acid sequence. Many amino acids can be coded with variant codons, I guess if repetition were a problem in a particular gene natural selection could step in.