The per sequence quality score report allows you to see if a subset of your sequences have universally low quality values. It is often the case that a subset of sequences will have universally poor quality, often because they are poorly imaged (on the edge of the field of view etc), however these should represent only a small percentage of the total sequences.
If a significant proportion of the sequences in a run have overall low quality then this could indicate some kind of systematic problem - possibly with just part of the run (for example one end of a flowcell).
A warning is raised if the most frequently observed mean quality is below 27 - this equates to a 0.2% error rate.
An error is raised if the most frequently observed mean quality is below 20 - this equates to a 1% error rate.