I've occasionally heard the credibility of popular historical books and authors called into question in part because they rely heavily on secondary sources. I also remember in my high school AP history classes they also mentioned this.
I'm having a hard time seeing why this is considered a problem. Obviously, if you are an academic historian writing for an academic audience then it is best to know and cite primary sources.
But, if somebody is writing a book or making a podcast for popular consumption on a period of history, and the secondary sources are a representative sampling of contemporary academic historians on the topic, shouldn't it be broadly accurate? Isn't that good enough?
No, it isn't good enough. Have you ever played the game of "Chinese Whispers"?
When studies or reports are used as a basis of a paper the historian presents it in a particular way so as to support his view (or undermine someone else's). When that paper is then used as if it is a primary source, errors and distortions can develop.
This is the basis for the "History Wars" in Australian academia. One historian (Windschuttle) conducted a detailed review of primary resources which he expected to support the then consensus view of a group of contemporary academic historians. The result of this was that he accused them of relying on secondary, tertiary, and greater, sources, grossly distorting the details that occurred. In particular, he said they referred to primary resources, by using tertiary resources to quote primary resources that proper research showed either did not exist, (eg newspapers that were out of print at the time or had not yet begun to publish) or could not have witnessed the occurrences (because they were not yet in the country or their letters were claiming to report hearsay).
Note: Windschuttle didn't call it "Chinese Whispers"
You have to understand in addition to PinkGayWhale's post that there isn't a single way to look at history and that there are differing accounts. For one particular instance is the Boston Massacre. If you took the British Captain Prestons report then you could argue that the American Colonialists instigated a riot and the British soldiers were defending themselves when they were attacked with stones, sticks, ect. when they were simply trying to keep order. However if you take Samuel Adams perspective the colonialists were wrongly attacked and although they were unruly they were not anywhere near a riot but the lack of professionalism in the British soldiers is what led to the massacre of colonial citizens. You could take a secondary source that used primary sources from either of these views without truly understanding what you're talking about and in some cases if one was wrong then it wouldn't be broadly accurate at all but simply what happens when you use a secondary source that isn't accepted within academia.