More rare mechanics that don’t map onto any other games I can think of…
Caylus - Provost / Bailiff
Fresh Fish - Expropriation (this doesn’t feel that unique… more like using a completely opaque rule to accomplish something very mundane in a way that works incredibly well)
Würfel Bohnanza; Ganz schön clever - Using the active player’s unused dice in a Yahtzee-style dice game (maybe this happens in some more traditional dice games, not sure)
Schnäppchen Jagd - optional trump suit??
Mamma Mia - memory + unknown information (other player’s hands). Uwe Rosenberg is showing up a lot in this list.
Pax Porfiriana - Players can take an action to speculate on market cards. If those cards are purchased, they money goes to the player instead of the bank.
John Company - promise cubes
Closed economic systems… The Great Zimbabwe, Pax Pamir, and Traumfabrik all slosh money around (mostly) without creating or destroying it.
Giving the majority shareholder sole control of something only happens in 18xx and probably some other train games (and is probably the defining characteristic of a ‘train game’ for some people).