Problems typically encountered with data likely fall into three categories: aesthetic, substantive and perceptual.
Since every individual brings the lens of their own life to every inference it's shocking there aren't more, but simplification of categorization seems reasonable within this scope.
But it is more likely that we are incorporating one or two of these pillars and failing for the third to uphold the same standard than it is that a visual has failed entirely at one or all three. As mentioned it is more common to fall short on the use of good data than it is to implement bad design, though not impossible.
Hard and fast rules seem to weaken the further we deviate from the standard, so while Tufte lays out principles, sometimes the best implementation is the rebellious breaking or bending of a rule, in exactly the right way with exactly the right data that makes for a successful representation.
But when manipulating data to infer an idea, as much considered need be applied to the design choice, as the mechanism and form of display, as the intentional presentation. I find it particularly interesting that in this quest for the proper balance of all three, there is a 'tour de force' in Minard's "Napolean's Retreat," which even then is an elusive, perfect storm that is more the exception than the rule.
Nonetheless, Tufte's timeless message on Graphical Excellence (1983) holds true as principles to always consider:
Graphical Excellence is the well-designed presentation of interesting data-a matter of substance, of statistics, and of design... [It] consists of complex ideas communicated with clarity, precision, and efficiency..[It] is that which gives to the viewer the greatest number of ideas in the shortest time with the least ink in the smallest space... [It] is nearly always multivariate... And graphical excellence requires telling the truth about the data.