There are indeed rare instances of recordings in which the L&R channels are in opposite phase. This was done in the late 70s and early 80s to create a cheap "spatial sound" effect (like the "surround" button on low-end hi-fi systems of the time), and on such recordings, computing the average of the left and right channels gives a null output. Some stereo effects (like chorus or reverb) would also make a recording sound less lively or flatter after a mono conversion, but this doesn't really qualify as noise. All these are rare problems, and averaging the L&R channels is the standard way of converting from stereo to mono. In the past I've worked on a system that handled large catalogues of audio files, and my approach was to check whether the energy of the average of the channels was below a certain fraction of the energy of the individual channels ; and if so, used the difference instead of the sum as a mono conversion. Ideally you could compute the cross-correlation between the left and right channels to find the lag at which they are maximally correlated, and delay one channel by the lag before the mixing so they are maximally in-phase with each other, but this is overkill for just handling the 15 or so tracks out of 100,000 that had a massive phase inversion problem - to give you an idea of the rarity of the problem...
The most obvious error is converting from 44kHz to 22kHz by skipping every second sample. This will alias all frequencies in the 11kHz - 22kHz range, and will make the downsampled recording sound "metallic", "crunchy" or "gritty". A proper way of downsampling a recording is to first apply a low-pass filter to remove all frequencies above half the target sample rate ; then decimate (skip every second sample).
