Barcode scanners use visible light -- typically a weak HeNe laser for their operation. The light is scanned by a rotating mirror so that the spot spend very little dwell time in any position.

While I could not recommend you looking directly into the scanner light, many studies have concluded that there is no danger to your eyes. Red light is easily stopped by virtually any clothing and at that intensity should have no effect on your skin.

A laser is used merely because it is easier to direct the beam as it is a single color. Some more recent scanners use infrared light which is not visible, and for which the same arguments above apply.

I cannot imagine a mechanism for genetic damage from these sources. This does not mean it is impossible, but it is far less likely than mutation from any number of natural causes (like breathing oxygen).