Impact of holding non-TT positions on potential for a TT position Is there any (negative) effect of prior holding of one or more non-tenure-track (TT) positions on the potential of being hired (and promoted) at a TT position at a university (mostly interested in US)?
In many academic fields it has become the norm for new PhDs to work in post-doc, visiting assistant professor, or other temporary non tenure-track positions before moving into a faculty position.  This is normal and expected. It should be obvious how a research post-doc will help you to gain experience in research.  For new PhDs with limited teaching experience, a good visiting assistant professor position can help with gaining teaching experience. 

However, there's a difference between a research oriented post-doc and a long term full time (or worse part time) non tenure track position as a lecturer.  In the latter case, you will have little opportunity to continue working on research and may be put to work teaching very low level courses.  It can be very hard to work up from such a position into a tenure track position, and the longer you do it, the worse it will look on your resume.    

Even with good research post-docs and visiting assistant professor positions, there's a limit to how many years you can do this work before you'll be seen as having failed in your academic career.  Too many years of post-doc experience is worse than having too little experience.