How to know whether s-p mixing will happen in heteronuclear molecules?
I don't think you can know, a priori, whether or not s-p mixing occurs without first having some experimental data.  I'll use water, a triatomic molecule, as my case in point.  

For over 50 years students have been told that water is roughly $\ce{sp^3}$ hybridized.  The general description is that there are two equivalent O-H $\ce{sp^3}$ sigma bonds and two equivalent lone pairs, also in $\ce{sp^3}$ orbitals.  The lone pair - lone pair repulsion is greater than the sigma bond - sigma bond repulsion, so the lone pair-O-lone pair angle opens up slightly and the $\ce{H-O-H}$ angle closes down to the observed 104.5 degrees.

With the advent of photoelectron spectroscopy it was found that the two lone pairs in water were not equivalent (2 signals were observed for the lone pairs).  Now, the hybridization of water is described as follows:


2 $\ce{sp^3}$ O-H sigma bonds
one lone pair in a p orbital
and the second lone pair in an $\ce{sp}$ orbital


If chemists knew how to predict s-p mixing, it wouldn't have taken them over 50 years to understand how they mix in water.