On that note, do we know if CD players get all the bits off a CD? What I mean by that is does the laser read everything on the CD or just most of the data and extrapolates the rest?
Error correction gives you the actual original data, it doesn't extrapolate anything. It's only in cases where error correction fails that the output diverges from the original.
You'll know when that happens. You then hear various artifacts, depending upon the problem and the design of the hardware. It could be muting, pops or clicks, skipping, etc. But things have to be pretty broken before these sorts of artifacts show up.
With a normal CD player (or transport and DAC, etc.) and CDs in decent condition, error correction fully corrects any flaws. (This doesn't mean that the conversion to analog is flawless, but when you're still in the digital domain you have data that is identical to the original.)
I do have to note that "identical" and "original data" may not be exactly true. There can be slight differences, but they are smaller than we can perceive. Nothing is perfect, but this comes pretty close.
