On my first extended visit to London fifteen or so years ago, I noticed a front-page headline on a (legitimate) newspaper that read something along the lines of: RANDY ANDY’S BAWDY JAPE. The article that followed reported (using anonymous sources) that Prince Andrew had apparently made an off-color joke at a party.
Thus was I introduced to the concept of silly season, which the Oxford English Dictionary dates to 1861 and defines as “the months of August and September, when newspapers supply the lack of real news by articles or discussions on trivial topics.” (The Randy Andy article was actually printed in a sort of subsidiary silly season, the period between Christmas and New Year’s Day.)
The phrase has been picked up and as far as I can tell broadened in the U.S. in recent years. That is, it doesn’t primarily refer to silly newspaper articles–in that regard, every season is silly season–but to idle or unsubstantiated speculation in politics and sports. For example:
- “The silly season has officially begun. The start is defined by a sudden desire among political reporters to speculate about who might be chosen by a presidential candidate — in this case, Mitt Romney — to be the vice presidential nominee.” (New York Times, June 21, 2012)
- “What [Matt] Kenseth and [Denny] Hamlin did last week is show that NASCAR’s traditional “silly season” — that time of year when drivers jump from team to team — isn’t so silly anymore, and may never be that way again.” (Washington Post, July 2, 2012)
- “The silly season, aka free agency, begins today at 9:01 p.m., Pacific time, and Lakers general manager Mitch Kupchak figures to be busy.” (Los Angeles Daily News, June 29, 2012)
notoneoffbritishisms.com 
It was also a term used in The Turks and Caicos Islands for the hot summer season. The Provo people used to call it that.
I recall reading a short science-fiction story back in the fifties (the golden age of s-f) entitled, “The Silly Season”. The setting was a newsroom, I think.
The silly season typically coincides almost exactly with Parliament’s summer recess. With the politicians away, the political journalists have nothing serious to report on and find themselves filling space with trivia. Once political fisticuffs resume in the House of Commons, the silly season abruptly ends and normal journalistic service is restored.
“The silly season” actually refers to mid to late spring when fledglings join their parents in food hunting. Naturally these inexperienced birds have no idea of how fast cars travel and often fall victim to these metal monsters. By mid May the silly ones that were destined to die have already done so, and those that have survived now know better.