Example practice problems and small real problems:

• Fermi estimation of everyday quantities (e.g., "how many minutes will I spend commuting over the next year? What's the expected savings if I set a 5-minute timer to try to optimize that?);
• Figuring out why I'm averse to work/social task X and how to modify that;
• Finding ways to optimize recurring task X;
• Locating the "crux" of a disagreement about a trivia problem ("How many barrels of oil were sold worldwide in 1970?" pursued with two players and no internet) or a harder-to-check problem ("What are the most effective charities today?"), such that trading evidence for the crux produces shifts in one's own and/or the other player's views.

Larger real problems: Not much to point to as yet. Some CFAR alums are running start-ups, doing scientific research for MIRI or elsewhere, etc. and I imagine make estimates of various quantities in real life, but I don't know of any discoveries of note. Yet.