Obviously, the Apollo astronauts had the shiny gold visor things, but I’ve dug up this video clip from the NASA archives:
(transcript here:
http://www.hq.nasa.gov/office/pao/History/alsj/a17/a17.sta6.html
mission time beginning: 165:00:47
One astronaut is clearly seen with his visor up, face visible. He then turns directly to face the sun (note the shadows). How dangerous would that be to his eyes and his health?
Well, if you were wearing a space suit, I’d say that would be a big “yes”. 
Serious answer–
I suspect that with brief exposure the risk would be low.
But, let’s wait for somebody to come around & correct me, hmmmm?
Read “weren’t” for “were”.
:o
Well, ground control told the astronaut (Cernan, Schmitt?) to lower the gold visor, so I guess they were concerned about it. Unless the clear visor had some jçkind of radiation shielding the guy would be getting quite a bit of UV radiation for starters.
Well let’s see. Our atmosphere protects us from much of the damage that can be done from the sun’s rays (ozone and all that stuff). The moon has no atmosphere.
Without a space suit you will very quickly fry on one side and freeze dry on the other.
[sup]and fizzle when the two meet.[/sup]
The atmosphere does stop a fair bit of the Sun’s UV, but if you’re staring straight at it, the danger is mostly just from the high intensity. Ever burn ants with a magnifying glass? That’s what you’re doing to your retina when you stare at the Sun for too long. Very little of the Sun’s total radiation is blocked by the atmosphere, so I wouldn’t expect the immediate danger to be much larger on the Moon than it is here. In other words, you could glance at it, as long as you didn’t stare.