I'm much too cheap to pay $44/year for a subscription to Bicycle Quarterly. Their back issues are also expensive. But someone offered me about 10 years in exchange for about $40 after shipping, so I jumped in and read it all. This is not the intended way for people to read the magazine, but I figured it'll give me some insight as to what the magazine's all about. I was not wrong.
First of all, Bicycle Quarterly should be renamed "Jan Heine's Quarterly Opinions, Reviews and Randonenuring Adventures." Nearly every article in the magazine is written by Jan Heine or one of his friends, with a few scant submissions from other people here and there. To my surprise, most of the photos in the magazine are pretty bad. After reading a few of the trip reports, I realized that it's because Jan Heine is not a bicycle tourist. He's a Randonneur, specializing in events where you ride a long distance with little or no sleep to a schedule. Well, if that's your goal you're not going to try to take beautiful pictures, and in fact, at night it's unlikely your photos are going to be any good anyway.
I have no idea who the magazine is aimed for. There's always an article introducing some new technique (like jumping curbs) to the reader, but I imagine most people who read the magazine already know how to do most of the things he describes. There are reviews of bicycles, but they tend to be of reviews of bicycles that are set up like Jan Heine's own favorite bikes. For instance, all bicycles are reviewed with 650b wheels (and 42mm tires), even bikes that would come in 700c sizes as well. The interesting thing is that the market for 650b tires seems to have been shrinking. When your preferred size is losing favor in the market you might want to rethink pushing it to your audience as you could lose credibility. (Having said that, I'm still doing friction shifting and rim brakes, so maybe his audience is like that but about 650b wheels)
Heine talks a lot about tires. Wider is better, and supple tires are best. The issue is that you have a hard time finding really supple tires at wider than about 32mm tires, so he formed another company (Compass Cycles, now Rene Herse) to supply those tires. The problem with his tire testing is that the sample sizes are really small, and the fact that his tires cost more than $90 for the extralight models mean that most people aren't going to be riding them.
Heine also talks a lot about frames and what makes a frame "plane." The term comes from boats where a hull could rise out of the water and "plane" and reduce drag, but his use of it in cycling bears no resemblance to what happens on a boat. Basically, the claim here is that certain frames under certain riders, will flex in such a way that the cyclist can sync with the frame, allowing the frame flex to return energy to propelling the bike up the road during pedal dead spots. If I was unhappy with his tire testing methodology, his statement about planing and cycling comes with next to no evidence. It's all subjective, and there's no attempt to generalize his experience for any other rider (who doesn't have the benefit of hundreds of different bikes to ride, including many custom frames) to figure out what planes and what doesn't. He makes general statements like: "Use lighter tubing for top tubes and down tubes, and stiffer chainstays". Go ahead and build a few bikes like that and figure out which ones planes and which ones do not. Don't have the budget for it? Me neither.
There's an obsession with "rinko" cycling in Japan. (No surprise, Heine's wife is Japanese) Here's the deal, I've ridden in Japan, and it's decent cycling, but nowhere close to what you can get in the alps, where the train systems in Germany, Austria, Switzerland and Italy do not insist that you have to take your bike apart and stuff it into a bag to get on a train.
There's a time when he and his wife tries a really old tandem built by Rene Herse in the alps. But they have crappy gearing and don't do any of the rough stuff. It's all very shallow, because unlike the single bike reviews, Heine has never tried a modern tandem with gears low enough to climb steep stuff with his wife.
All in all, I'm glad I wasn't paying $44/year for a subscription (chances are I would have given up after a year when I noticed nearly everything in the magazine was written by Jan Heine). I'm not sure a typical cyclist reading this magazine will get much out of it, and I've already summarized 10 years of articles for you.