Should all CD-RW drives be able to read all CD's? Yes, in a perfect world.
The question of which blank discs are used is a big issue. It is possible for an older CD player to not be able to read certain discs. The speed at which they are burned may be an issue, the length of the disc may be another issue, the dye of the disc may be a third issue, and sometimes certain discs don't mix with certain drives. There doesn't have to be an explanation, they just don't mix occasionally. Take a look at the Media Compatibility List
to see some examples of discs that simply won't work well with certain drives. '--' denotes unsuccessful burns (maybe even reads too, who knows?).
To narrow down your specific case, if you have tried reading a certain disc in your Arrgo drive before and it worked fine, but for some reason now the drive won't read it, it's entirely possible that the drive is at fault; especially since it is making very strange noises. To be sure that the disc is OK, try having another drive read it. If a certain disc was never able to be read in the Arrgo drive, then I would chalk it up to incompatibility.
No, I like women.