A classic “false economy” is when you get something cheap that turns out to cost more than you thought – a car that breaks down all the time, shoes that fall apart quickly. But cheap things can cost you not only money, but also time and the goodwill of others.
As a teenager I was suspicious of adults because they seemed less idealistic than young people. I didn't want to become like them. But now I see that it wasn't just that people become more selfish as they age, but also that they have a better understanding of false economies. Some sacrifices that seem noble to adolescents are recognized by adults as wasteful.
I was talking to a friend who gives away a lot of his money but who bit the bullet and got himself a good suit. He realized that there were circumstances where he needed to talk to important people about these ideas, and having a good suit was part of being credible. Part of him resisted spending the money, but there are times when spending money lets you do a lot more good than donating it.
Saving money may be a false economy if it costs you time. If you would be doing something worthwhile with the saved time, it may be better to take faster, more expensive methods of transit. (If you wouldn't be doing anything worthwhile with your time, maybe you should find something.) An easy-to-use phone and laptop are another good investment.
Look out for "savings" that tax your relationships with other people. I spent a summer as a houseguest at a stage when I was very concerned about the fuel it takes to heat water, and the family I was staying with found it bizarre that I wanted to wash the dishes in cold water. I should have just done things their way to avoid the conflict – maintaining good relationships probably allow you to do more good than saving a bit of fuel or whatever you're trying to avoid.
I tell myself all this, but I still find false economies hard to avoid. (Years of skinflintery are hard to overcome!) I keep telling myself I'm going to spend some money and get decent versions of things I use all the time, like socks and pens. Then I succumb to finding the cheapest ones and usually end up dissatisfied. I think I need to set some kind of price floor before looking. Or maybe have a rule that I can only buy ones I wouldn't be embarrassed to give to a friend.