"Bug" is an industry term for an on-screen graphic, usually a network logo, superimposed on a TV program. In Warner Wolf's case, all of his Plays of the Week featured a bug of the CBS "eye" logo in the upper left corner. This would deter any potential copyright infringers from stealing Warner's hard work -- and even if they did, CBS would get the publicity (still pretty important in an era of just three television networks).
On-screen graphics themselves weren't new, but in television's early days they were pretty primitive. Producers pointed a camera at a piece of black cardboard with white text, and then faded it with the live image to superimpose a title (for example, during the Beatles' appearance on the Ed Sullivan Show in 1964). In 1968, covering the Democratic and Republican conventions, CBS didn't want to be fiddling with pieces of cardboard during live broadcasts, so they helped to pioneer the first ever digital character generators.
These devices became more and more sophisticated through the years, but they all had one thing in common: the graphics came on the screen, and then they came off. When did the bug become a permanent fixture of our TV programs?
According to this Wikipedia page, CBS began superimposing the bug on all its newscasts in 1990. They wanted business travelers to instantly identify a CBS station anywhere in the country. However, Warner's Plays of the Week did this as early as 1985 -- meaning he probably pioneered the era of buggy TV!
Live sports also played a role in the evolution of the TV bug. Originally, sports broadcasters only posted scoreboard graphics occasionally; if you started watching in the middle of a game, you'd have to ask your friends what the score was, or how much time was left. Scroll through this broadcast of Super Bowl III, and see if you can find any on-screen graphic, other than the clock at the very end. Here's another example from a BBC soccer match in 1979.
When Fox began broadcasting NFL football in 1994, they introduced the FoxBox: an on-screen scoreboard graphic that stayed permanently superimposed in the corner. Since then, broadcasters have continually pushed the envelope of information overload; compare that 1969 NFL broadcast with a typical NFL broadcast of today.
Now all TV has gone the way of short-attention-span theater. Desperate to maintain even the tiniest slice of brand awareness, TV networks put bugs on everything -- cramming them with logos, tickers, clocks, animated promos, scoreboards, and in the online era, websites and hashtags. This was masterfully lampooned in 1999 by Saturday Night Live, in a prescient instance of life imitating art.
While we may put the blame at the feet of Warner Wolf, CBS, or Fox, I like to think that if my dad had just continued showing 8mm films at his paving conventions, none of this would have been necessary.