The least controversial one I can think of is the thought that Pi has an end.If we find the end of Pi, we have an exact ratio of the diameter to circumference of a circle, and the roundness of an arch is now nonexistant, having been reduced to a series of infinitesimally small jagged lines like pixel art. It's like finding the end of infinity, when you get there, you can always add 1 to it, meaning it will still go on; in this case, you can always make the little jaggies smaller, making the circle even more round. Pretty much the only result of proving Pi has an end is proving that we do, in fact live in a matrix (as we now know the resolution of life).
Other than that, here are some environmental concerns people get wrong:
Recycling oftentimes creates more air pollution than creating something from scratch. The only real benefits to recycling is price point (such as in metals), Ecosystem preservation (such as paper and cardboard), resource preservation (metals again, and oil in the case of plastic), and reduction in landfill use. Due to transportation and refining practices, recycling tends to create a lot more greenhouse gasses than initial production, meaning that recycling to stop global warming is ridiculous (although, like I said, there are still plenty of benefits).
Relatedly, most "Bio-degradable" stuff (such as those Sun-chip bags, for example), will not, in fact, degrade, because they get packed into such a small and dense spaces they get no air or degraders to come in and clean it up, making the ultimate result not at all more eco-friendly (and all the more expensive. Hooray!)
Electric cars do not really help the environment as much as people think. Even removing the production costs, most of the electricity in the world is run on coal and other hydro-carbons, and the conversion to electricity that can be used for energy is more inefficient than a gas engine at this time, meaning that for the same mileage most electric cars have a bigger carbon footprint than gas. Then, gas motors are almost made fully of recyclable metals, whereas electric motors and their batteries are made from lots of unrecyclables and hazardous materials we don't want in the environment, meaning their long-term impact is horrible as well.
And, as much as I love the Fallout series, it has done nothing but help several nuclear fallacies:
Radioactive materials cannot make other things radioactive under normal circumstances (such as with nuclear fallout). While there's always a risk of the material contaminating water or something along those lines, it cannot make it radioactive, and if it did, it would not stay so long.
Dangerous nuclear material has an incredibly short half-life. While all radioactive material is dangerous to some degree, the dangerous kind used in bombs and such would have died out long before the 200 years or so that have passed in the Fallout timeline.