Re: Is DNA often drawn incorrectly?

A double helix is not just a ladder twisted right? It is more like a ladder wrapped diagonally around a cylinder. Is that correct? How important is this distinction?

Right; correct; yes, it is; this distinction is the foundation of molecular biology.

As you've pointed out, the rungs (basepairs) of the DNA ladder are offset from the helical axis. The result of this is that there is a more-open side of each rung resulting in a major groove in the helix and less-open side of each rung corresponding to a minor groove. (There are some good diagrams of this at Doug Brutlag's Site at Stanford.) The situation of the basepairs in the helix is such that a specific edge of each base is always presented to the major groove, which allows proteins to read the sequence of the DNA without having to open the strand. With only a handful of key exceptions, DNA-binding proteins - like transcription factors and endonucleases - bind to the major groove and interact with each other based on the spacing between grooves. Without the major groove, the orientation of the basepairs would be uncontrollable, and the specificity of these proteins would be lost: no more restriction enzymes; no more gene regulation; no more molecular biology as we know it.

And finally: yes, DNA is usually drawn incorrectly, especially in science fiction movies about genetic manipulation. I think there's a social commentary there somewhere about the pervasiveness of scientific illiteracy in our country - especially in Hollywood where they can barely spell "DNA" - but I'll leave that to you to make.