What is it? Edit
The concept of a persona itself is based on the idea that one has a genuine personality as well as a professional personality.
This applies to everyone, not just famous people; grocery store workers, for example, tend to have an extra smiley facade in order to appease their idiot customers.
Persona in and of itself is not bad per se.
Why is it bad for the show, though? Edit
There are many aspects to what makes a good interview and a bad interview. One big one, in the opinion of Joe and especially Lars, is whether a guest is willing to "let their hair down" and give people a look behind their public persona. If they are, the episode tends to feel a lot more genuine.
Obviously this is not a guarantee; some people, on their deepest level, are boring. However, most notable people (as in, the type of person interviewed on the show) did not get to where they are in life by being boring. So the correlation is almost 100%.
Lars and Joe have refrained from giving any examples of guests who kept the persona up (and thus led to a mediocre episode), ostensibly due to professional courtesy. However, they have cited examples of guests who did not, like TeeKlef and RoboRob; Lars considers the latter two to be examples of the best episodes of the show.