DNA as a digital storage medium; sequences algorithmically avoided for safety reasons (or should be)?
Yes, there could be sequences that a DNA based system could not store handle/very well: repetitive DNA sequences.

Not only do such sequences make a lot of problems during the sequencing ('reading of data'), but they are also more prone to form secondary structure elements like loops, since repetitive DNA can bind to itself in various different ways. This means that similar to natural occuring repeats they are more likely to mutate during DNA amplicifation (the number of 'copies' can quite easily change), which makes the 'data' more instable.

A possible way to solve this problem would be to use specialised data formats that avoid as much Repetition of data as possible (similar to how zip or jpg files work)

Otherwise I agree with Nathan, that DNA by itself is not dangerous (since it won't do anything outside of cells, and the bacteria used in molecular biology are generally harmless unless you start eating them in large quantities or otherwise getting them in your body). The possibility that the DNA could somehow code for toxic proteins is very very low, and you could just check that the 'data' in the DNA does not form a protein by chance anyway.