Once during a rehearsal of Blockbusters, Bill said something to the effect of "If only I knew the answers to half the questions I've asked over the years". This tells me that while he may have been fine at word games, Q&A games such as Blockbusters or Jeopardy! were not his forte.
Or that Bill routinely downplayed his own abilities so as not to come off like a know-it-all.
I've mentioned this before, but pop culture seemed to be a weakness of his. The week Ludden came back to P+ after Uncle Bill filled in for him, one of the puzzles was
Laverne And Shirley. Cullen could get the passwords to the puzzle with little trouble, but openly lamented as he was trying to figure the puzzle out that while he knew it was a TV series he was bad at coming up with titles like that.
On the other hand, he got the puzzle "Senator Joseph McCarthy" after one clue, so while pop culture might have been a weakness, other subjects seemingly were strengths.