Even though I could not follow it in places, I now at least know in general terms where to look for statistical errors and intentional stunts. The bad news in a sense is that I see these shenanigans everywhere now.
In that vein, How to Lie With Statistics
is a book everyone should read. It's not any kind of hardcore stats text; it's a quick read about the tricks you see in many, many articles, e.g. if some value changed from 893 to 899 and you want to make it look like a huge jump, you do a bar chart with the X axis equal to 891, or cherrypicking data - picking start/end dates, or data from selected cities, where the selection influences the results. As you say, you see those tricks all the time.