DAMBE (free software) under the "graphics menu" has plot transitions and transversions vs F84 distances. 

This is commonly done with a scatter plot of pairwise genetic distances.  For each pair of taxa, you use some subset of nucleotide sites for the y-axis, and all the sites for the x-axis.  The subset could be either the transition substitutions, the transversion substitutions (these first two are commonly plotted together; and some software is set up to do this for you), a codon position, ribosomal loop sites, or whatever you like.  If there is saturation, the best-fit line of the plot will level off as you go left to right.  If there is no saturation, the best-fit line of the plot should linearly increase from left to right.  

Some use the uncorrected p-distance for the x-axis distances, while others use a model of nucleotide substitution.  Using a model seems a bit circular if the reason you are doing the plot is to see if a model is needed to account for unobserved substitutions.  

DAMBE (free software) under the "graphics menu" has plot transitions and transversions vs F84 distances. 

I would highly recommend Brian's suggestion. DAMBE is fantastic and easy to use. 

I have a phylogenomic dataset of ~2200 loci which I would like to sort into those where the third position is saturated, and those, where it is not. Does anybody know, if there is an implementation of DAMBE or of the algorithm used therein to apply over multiple loci automatically? Or may be a command-line that can be wrapped to loop over multiple inputs? The solution proposed above generates a fine informative plot for single locus, but running it on a a dataset like mine is not feasible:-(

Thanks,

Alexander