Wheel Size - Look for wheels and tires labeled as 700c rather than 27” or any of the oddball Schwinn 26” sizes. There are few quality tires available, and switching to the much more common 700c from 27” size is possible but requires not only new wheels and tires, but likely new brake calipers to make up for the difference in diameter.
Dropouts - Rear dropouts that look like they are cut or stamped from a piece of sheet steel are a telltale sign of a low quality frame worth passing on. Look for cast or forged dropouts. If the dropouts themselves are lugged you are most likely looking at a very high end frame in its day, and one that should not be passed up.
Cranks and Bottom Bracket - It should almost go without saying, but one-piece cranks with an oversized bmx-style bottom bracket shell and cottered cranks that sport a press-fit pin to keep them in place are best left in favor of a square taper design.