On 'White Collar', Neal Caffrey is a con artist turned consultant for the FBI. When he asked his "handler", Agent Peter Burke, if he could run with the lead on a case, Burke snarked:
"Run with it? No, Barney Fife, you can walk very slowly."
This doesn't necessarily have to be a Zonk, just because a character on 'White Collar' mentions a character (and one of the most famous characters in all of Toobworld!) from 'The Andy Griffith Show'.
After Barney left the Mayberry police force (which consisted of only Sheriff Andy Taylor and his cousin Barney) in 1965, he moved to Raleigh where he became a detective. Who can say what may have happened during that time which could have thrust Ol' Barn into the national spotlight? There were some references in later episodes when Barney would return for a visit (and on 'Mayberry RFD' when he came back for Andy's wedding) that Raleigh didn't turn out as Barney had hoped. So any such headline-making case would have to have occurred after those appearances. Or it could have happened more recently, at any time after Barney had come back to live in Mayberry as seen in 1986 in a reunion TV movie. I'm afraid that such an event that would get Barney Fife into the national headlines and on the various news networks around the country was probably based on Barney's natural ineptitude. This would splain why his name is often used in a derogatory manner. (A "Barney Fife" would be a reference to inept law enforcement, in the same way as a "Lewinsky" would refer to a specific sex act. Just thought I'd throw that out there.....)
So all in all, it would not be a discrepancy, a Zonk as it were, for Peter to call Neal a "Barney Fife". We just don't know the reason why Barney became so nationally well-known.
Well, as far as that Zonk is concerned, I think I was able to nip it; nip it in the bud!
I could use a Lewinsky after that....