Impact factor generally is a credibility factor or at least I do not know of any journal in my field where there is a low-credibility journal with a high impact factor, although there are some specialist journals - e.g. instrumentation - which are highly credible but with a low impact factor. Generally speaking though anyone in the field worth their salt will know which the good journals are and where a paper is published generally does have a large impact on how we regard its quality.
Impact factor seems like more of a measure of "this is important and consequential", rather than "this is free of fraud". Anyway, there have been multiple instances of fraudulent papers coming out in high-prestige journals with extremely high impact factors (Nature, for one).
I do not see a good way for a "credibility factor" to be calculated in an objective manner that would not have significant negative repurcussions e.g. counting the number of retractions would be bad since it would encourage journals never to retract papers.
Right, that's why retractions shouldn't count against you. If anything they should boost your score (if done in a timely/responsible fashion).
I don't know exactly how to "measure" fraudulent research or what criteria should be used-- but obviously the PNAS authors figured out a way, or they wouldn't have been able to do a "statistical analysis" of the problem.
Similarly even the best intitutes can hire rogue researchers - or more commonly have bad grad students or postdocs - and enouraging journals to accept anything from any researcher in a "respected" instistute to boost their credibility would be bad too. Also papers in many fields cannot and do not have a single "primary" author.
The credibility score of the institute would be calculated separately from the credibility score of the journal and of the researcher. That's why I suggested multiple scores. In other word, it wouldn't automatically boost the journal's score to publish results from a high-credibility institution-- except indirectly, by reducing the probability that they are publishing a fraudulent paper.
Look, there are all sorts of fine points to debate over, when it comes to exactly how to calculate scores. But that doesn't mean it's a bad idea.