Here are some that came to mind:
Equivalence. Basically, the idea that two things can be functionally equivalent (or close to equivalent) even if they look very different (and conversely, that two things can be superficially similar but functionally quite distinct). For instance, paying off a credit card at 10% is equivalent (as a first approximation, at least) to investing that money with a guaranteed 10% rate; once one sees this, it becomes obvious why one should be prioritising paying off high-interest credit card debt ahead of other, lower-interest, debt reduction or investments (assuming one has no immediate cash flow or credit issues, of course). Not understanding this type of equivalence can lead to real-world consequences: for instance, in the US there is a substantial political distinction between a tax credit for some group of taxpayers and a government subsidy to those same group of taxpayers, even though they are almost completely equivalent from a mathematical perspective. Conversely, the mistaking of superficial similarity for functional equivalence can lead to quite inaccurate statements, e.g. "Social Security is a Ponzi scheme".
Counterfactual thinking. The ability to take a counterfactual hypothesis and deduce consequences from it (or, in some cases, absurdity) is common in mathematics (and in a few other disciplines, such as law or fictional writing) but not always among the general public. For instance, to provide evidence of a claim such as "A always leads to B", it is not enough to produce examples in which A and B both hold; one has to show that the counterfactual situation in which A holds and B fails is necessarily either impossible or implausible. Or for a more mundane example: to get a true sense of how impressive it is that, say, your daily horoscope seems to be eerily accurate, one should analyse the plausibility of a counterfactual situation in which the type of statements one typically receives in a horoscope turns out to be clearly inaccurate.
Quantification. Cost-benefit analysis is basically impossible to do right unless one has at least a rough order of magnitude for each of the costs and benefits. With only a qualitative understanding of the costs and benefits, one may end up expending far too much time and money to avoid a tiny amount of risk or cost, or conversely skimping on a negligible expense which would protect against a high-probability catastrophic event in the future. Also, because one cannot easily adjudicate between costs and benefits when one has a qualitative mindset instead of a quantitative one, there is a psychological incentive to "simplify" the problem by downplaying or ignoring the costs of actions that one wishes to take, while downplaying or ignoring the benefits of actions that one wishes to avoid.