As with most endeavors, there are plenty of ways to make bicycle science bad. There are a few ways, however, that seem to be more popular than others. Here are some of the most common:
1. Ignoring or misinterpreting previous work
Most of the examples itemized in the posts on this site make this mistake. The UW-Madison Physics Department writes as though it were in a vacuum, while Physlink.com cites a useful work and then comes to the opposite conclusion of the author.
Despite flaws in its final analysis, Jones’ 1970 Physics Today article demonstrates the limited role of gyroscopic effect pretty clearly . Thus, anyone writing after 1970 that bike stability or ridability derives solely from gyroscopic effects or that bikes are almost impossible to ride without gyroscopic effects simply hasn’t done their homework.
2. Misinterpreting laws of mechanics
By far, the most popular law to flaunt is that of angular momentum, as demonstrated by Mental Floss.
Spinning wheels have no resistance to roll moments if they are prevented from precessing about the yaw axis. Instead, a roll moment causes the front wheel to precess in the direction of the lean, and the rear wheel, which is prevented from precessing by the frame and friction in the two contact patches, leans exactly as it would if it were not spinning.
A related misconception is the assertion that angular momentum is somehow conserved when riding a bike and this conservation of angular momentum is why the bike stays upright. Instead, a roll moment from gravity or a steer torque on the handlebars from the rider easily modify the angular momentum.
The next most popular law to flaunt is that of linear momentum, as demonstrated by Rider Education of New Jersey.
Linear momentum is a vector quantity and so the linear momentum in one direction, such as forward, has no effect on linear momentum in an orthogonal direction, such as to the side. Thus the increased linear momentum from going faster is not responsible for the smaller steering inputs required to maintain balance. Instead, it is simply the fact that a give steering input works faster, that is causes a larger lateral acceleration of the contact patches, if the wheels are rolling forward faster.
3. Providing no equations or calculations, no instrumented physical experimentation, or any other sort of validation
This is more of a problem with articles in supposedly peer-review journals, such as in the European Journal of Physics.
Certainly, not every article is intended for a technical audience, but every assertion still needs to be based on reality. Claiming the gyroscopic effect is responsible for so and so without even doing a back-of-the-envelope calculation to show it is possible is just blowing smoke.
Direct human observation is notoriously unreliable, especially of small behaviors combined with large behaviors, such as the steer angle of a speeding motorcycle. Even the Wright brothers observed that most bicycle riders do not realize that they apply a steer torque to the left in order to turn right.