Importance of publications if one decides to go industry after PhD?
Publications demonstrate several things such as:


Ability to conduct, complete, and document work
Ability to communicate clearly
Interest in broadening the field's knowledge
Interest in staying aware of the "state-of-the-art"


All of these are good attributes to demonstrate with a publication record.  Continuing to publish in industry is also valuable, but it is seldom "publish or perish."  

Regarding important factors: use elements of your Ph.D. to demonstrate that you can work independently to solve difficult problems.  A strong work ethic and ability to solve problems are key traits that employers are looking for.