What does it mean to "falsify" a theory? Well, you can't falsify a theory globally - even if it's shown to be false under some conditions, it might hold true far away or in the future. And almost every theory is falsifiable to some degree of precision, since almost every theory is just an approximation of reality.
What falsification really means - or should mean, anyway - is that a theory is shown to not work as well as we'd like it to under a well-known set of conditions. So since people have different expectations for a theory - some demand that theories work with high degrees of quantitative precision, while others only want them to be loose qualitative guides - whether a theory has been falsified will often be a matter of opinion.
But there are some pretty clear-cut cases. One of them is the "Econ 101" theory of the labor market. This is a model we all know very well - it has one labor supply curve and one labor demand curve, one undifferentiated type of labor and one single wage.
OK, so what are some empirical things we know about labor markets? Here are two stylized facts that, while not completely uncontroversial, are pretty one-sided in the literature:
1. A surge of immigration does not have a big immediate negative impact on wages.
2. Modest minimum wage hikes do not have a big immediate negative impact on employment.
George Borjas disputes the first of these, but he's just wrong. A few economists (and MANY pundits dispute the second, but the consensus among academic economists is pretty solid.
The first fact alone does not falsify the Econ 101 theory of labor markets. It could be the case that short-run labor demand is simply very elastic. Here's a picture of how that would work:
Since labor demand is elastic, the supply shift from a bunch of immigrants showing up in the labor market doesn't have a big effect on wages in this picture.
BUT, this is impossible to reconcile with the second stylized fact. If labor demand is very elastic, minimum wage should have big noticeable negative effects on employment (represented by the amount of green between the blue and red lines on this graph):
By the same token, if you try to explain the second stylized fact by making both labor supply and demand very inelastic, then you contradict the first stylized fact. You just can't explain both of these facts at the same time with this theory. It cannot be done.
So the Econ 101 theory of labor supply and labor demand has been falsified. It's just not a useful theory for explaining labor markets in the short term (the long term might be a different story). It's not a good approximation. It doesn't give good qualitative intuition. And it's especially bad for explaining the market for low-wage labor, which is the market that most of the aforementioned studies concentrate on.
What is a better theory of the labor market? Maybe general equilibrium (which might say that immigration creates its own demand). Maybe a model with imperfect competition (which might say that minimum wage reduces monopsony power). Maybe search and matching theory (which might say that frictions make all short-term effects pretty small). Maybe a theory with very heterogeneous types of labor. Maybe something else.
But this theory, this simple Econ 101 short-run partial-equilibrium price theory of undifferentiated labor, has been falsified. If econ pundits, policy advisors, and other public-facing econ folks were scientifically minded, we'd stop using this model in our discussions of labor markets. We'd stop casually throwing out terms like "labor demand" without first thinking very carefully about how that concept should be applied. We'd stop using this framework to think about other policies, like overtime rules, that might affect the labor market.
Sadly, though, I bet that we will not. We will continue using this falsified theory to "organize our thoughts" - i.e., we'll keep treating it as if it were true. So we will continue to make highly questionable policy recommendations. The fact that this theory is such a simple, clear, well-understood tool - so good for "organizing our thinking", even if it doesn't match reality - will keep it in use long after its sell-by date. That's what James Kwak calls "economism", and I call "101ism". Whatever it's called, it's not very scientific.