Error correction is standard for all CD's, as specified by Red Book. I did have a CD that was longer than normal length, that an old player wasn't able to load. Also I have a Samsung player that is extremely shallow, and CD's with a rib would get caught between the tray when the tray is being closed. But these are rare exceptions. Try bringing a CD you say won't play and test it out in the shop which you plan to buy from as a demo. It's possible the CD was destroyed by light (which I had before, from leaving on the car dashboard).
Red Book CD Format Explained
The term “Red Book” is named after one of the Rainbow Books, a series of books (bound in different colors) that contain the technical specifications for all CD and CD-ROM formats, such as the tracks, sectors, block layout, coding, and sampling.