"Quoins" are the exposed stone pieces that you sometimes see stacking up only on the corner of a building. They sometimes look like a zipper applied to the corner edges of a structure.
It is probably unfair to throw all of these in a single despicable category, but the abuses in the last 40 years are so egregious that only a complete moratorium on all mansard roofs will suffice to still the repulsion of most architects.
A mansard roof is unusually a full story of a building masquerading as a part of a roof. It is a gambrel/hip roof hybrid that brings the apparent mass of a building down a story or two by letting the "roof" start much lower down than the interior floor levels would typically indicate. Handled well they are a pleasing architectural solution to a vexing problem. Most often however, they are not so deftly deployed and instead of reducing the apparent mass of a building, they increase it with a gargantuan, bulbous forehead. These are not attics with quaint dormers sticking out, but rather massive toques with eyeholes sitting on top of otherwise rather elegant buildings. Or maybe not so elegant.
The term come from French Baroque architecture as often conceived by Francois Mansart, however many of the best examples come from the Second Empire period. Its popularity may stem from attempts to copy those examples or as a tax/code dodge - many municipalities tax a building based on the size from the ground to the base of the roof. Building height limitations also occasionally measure to a roof's midpoint. In both cases, the definition of "roof" is pressed with a mansard, arguing that the sheathing in roof materials meets the requirements.
The pet peeve stems from the truly horrible examples foisted upon the public in the last few decades. Mansards are almost always incompatible with more modernist design language and they take a very able hand in any scenario. So, for the sake of the collective built environment, I am going to advocate for a moratorium on mansards until at least 2020. By then maybe we will have figured out how to use them to enhance a building, not draw attention to its flaws.
Unless of course, you can make it over-the-top mansard-awesome:
another in a series of architectural pet peeves of mine, this one on painfully outdated electrical products and procedures in wiring a house
on the distinction between cement and concrete
another in a series of architect's pet peeves - in this case, fake masonry, the artificial stone and brick stuff masquerading as real construction
another in a series of architect's pet peeves - in this post, turrets on suburban American houses.