there is a very good research university (actually many of them; this is mathematics in the US) that have both tenure-track assistant professor open positions and lecturer open positions. I want to know what you think about applying for both. Ideally I want the tenure-track position, but the job market is tough, and I would also be happy with a lecturer position (which is much more teaching oriented). How would a hiring committee look at this? I am afraid that the tenure-track guys will say "Well, this guy/girl doesn't think he/she's good enough to get a tenure-track job because he/she is also applying for a lecturer position, so let's ditch him/her". At the same time, the lecturer guys could say "Well, it seems that he/she wants a tenure-track position but he will settle for a lectureship. We want someone more motivated."
There is a similar question here: Should I simultaneously apply for multiple jobs in different ranks at the same university? which is more about "post-doc vs. tenure-track". I think this situation is slightly different.