I use propensity score matching (PSM) with logit regression distance. What maximal propensity score (ps) distance in each pair of the treatment and control individuals can be allowed? What maximal difference between mean propensity scores of treatment and control groups can be tolerated?
This is a suggestion that you consider not using PSM as a matching algorithm.
Gary King has a very recent paper (July 2015) on Why Propensity Scores Should Not Be Used for Matching that is pretty compelling. His suggestion is that Mahalanobis distance functions be used instead. It's worth reading the paper for his development of PSMs as well as MD functions. Wrt your questions about cutpoints, King's suggestion, on p. 20, is that they "be arranged so they divide the space between the minimum and maximum values into equal sized bins," basing a final decision on an imbalance metric (details in a link to an earlier paper given in footnote on p. 19).
In this ICM webinar (Sept 2015), he explains all of this succinctly and cogently, graphically demonstrating the significant improvement in matching accuracy of MD vs PSM.
Some answers may be found in the following papers:
Austin P.C. Optimal caliper widths for propensity-score matching when estimating differences in means and differences in proportions in observational studies. http://onlinelibrary.wiley.com/doi/10.1002/pst.433/full
Optimal Caliper Width for Propensity Score Matching of Three Treatment Groups: A Monte Carlo Study http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0081045