The most useful skill I've developed has been in meeting immaturity (both in rationale and delivery) with maturity (ditto). I work in a heavily right-wing workplace that refuses to allow anything but Fox News on anything resembling a television. This is my training environment. Even in the presence of highly irrational and emotionally charged convictions, I've found that the ability to maintain an uninvested calm and slowly help my partner to make their argument better (through gradual consilience with reality) can result in ACTUALLY CHANGED MINDS. The first step seems, invariably, to point out those counterfactuals that back them away from absolute confidence; when presented as potential improvements ("You'd probably see greater success at decreasing the actual number of abortions if you could find ways to enable people to only purposefully conceive a child.") even a position they once reviled can seem outright tasteful. The key appears to be presentation of oneself as a potential ally, so as to avoid the "I must engage on all fronts" mentality that prevents meaningful engagement at all.
Related to: Tsuyoku Naritai! (I Want To Become Stronger), Test Your Rationality, 3 Levels of Rationality Verification.
Robin and Eliezer ask about the ways to test rationality skills, for each of the many important purposes such testing might have. Depending on what's possible, you may want to test yourself to learn how well you are doing at your studies, at least to some extent check the sanity of the teaching that you follow, estimate the effectiveness of specific techniques, or even force a rationality test on a person whose position depends on the outcome.
Verification procedures have various weaknesses, making them admissible for one purpose and not for another. But however rigorous the verification methods are, one must first find the specific properties to test for. These properties or skills may come naturally with the art, or they may be cultivated specifically for the testing, in which case they need to be good signals, hard to demonstrate without also becoming more rational.
So, my question is this - what have you become reliably stronger at, after you walked the path of an aspiring rationalist for considerable time? Maybe you have noticeably improved at something, or maybe you haven't learned a certain skill yet, but you are reasonably sure that because of your study of rationality you'll be able to do that considerably better than other people.
This is a significantly different question from the ones Eliezer and Robin ask. Some of the skills you obtained may be virtually unverifiable, some of them may be easy to fake, some of them may be easy to learn without becoming sufficiently rational, and some of them may be standard in other disciplines. But I think it's useful to step back, and write a list of skills before selecting ones more suitable for the testing.