I find the comment about eye damage little bit strange.
I calculated that the Betelgeuse has power output of 3.846e26 * 5e9 W (5e9 brighter than sun) ~ 1.923e36 W.
640 lightyears is 2.9979 m/s * 60 * 60 * 24 * 365 * 640 ~ 6.05e18 m.
The irradiance falling from Betelgeuse up to a sphere whose radius is the above number is then 1.923e36 W / pi*(6.05e18)^2 ~ 0.0167 W/m^2, and assuming the spectrum behavees similarly as the sun's, there is 25 % loss due to scattering. Earth based observer then has average irradiance of 0.0122 W/m^2 from Betelgeuse. If he is using Mark I Eyeball for viewing, the iris aperture is maximally about 8 mm with scotopic vision. This means he collects approximately 0.0122 W/m^2 * (4*10^-3)^2 *pi ~ 613 nW on the retina.
For the contrast, usually Class I or II lasers are limited below 1 mW of power. This does not pose a significant eye hazard as long as the laser is not pointed on the eye for a long time. To really damage the retina, optical powers of order milliwatts are needed. Because these lasers are also relatively well collimated and form about as small spot as the distant star, I think the comment about the potential eye damage is exaggerated.
However, there most likely is a strong difference of contrasts as the moon is relatively nice on the eye due to a larger size which provides some sort of averaging for the eye. For a distant star, it is small and black background will enhance the observed brightness. I could expect some kind of bright spot as an after image in the field of view, but I highly doubt any of those could do real damage to the eye.
Mika