It sounds like a stupid question until you are balancing 4 different projects with 6 people generating data, but how much responsibility do PIs have for the data produced by their trainees and how deep does one have to go to ensure due diligence? Look at the raw data? The analyzed data? The analysis methods? Is there a difference between new and seasoned trainees?
In more than a few places (an example here), DrugMonkey and others advocate for new faculty to get away from the bench and focus on running the lab rather than generating the data. I don't have a problem with the advice, but inherent in that is the requirement that the trainees generating (and almost certainly analyzing) the data be trusted to do so if the most rigorous ways they know how to.
Obviously, the PI has the responsibility to train the people in their lab to perform these analyses, but how much double checking should be done? A case in which the result is clearly at odds with expectation is an obvious example for follow-up, but rarely are cases of data mis-analysis (or worse, data fraud) that actually reach the PI, cut and dry.
For the most part, it is the inadvertent mistake that can skew results without raising suspicions. Removal of "outliers" for "better fit" (which, BTW, can be very sketchy), sample contamination between two close-related species, slight mis-alignment in a phylogenetic alignment, etc., etc. The careful and experienced trainee may catch these, but any lab is often made up of trainees with a range of experience and aptitude for recognizing subtle problems. It is not uncommon for even triple-checked data to be later found to contain a significant error, which gets us back to the original question: How deep into the data should a PI go to make sure the end product represents the proper quality of data?
I don't know the answer and I suspect that it becomes a case by case issue, but for the PIs out there, how do you handle this? For the trainees, how much does your PI check through your work?