If you were standing on the moon at such a place and time that you were looking at the Earth’s day side, and someone launched a rocket from a part of the Earth that you could see (say, the part closest to you), would you be able to see the launch occurring? If the rocket launched a satellite into a medium or high Earth orbit, would you be able to see the satellite from the moon? (For that matter, would you be able to see any satellites?)
And on a semi-related note, how bright would the illuminated surface of the moon be to someone standing on it without eye protection? Bright enough to hurt? Bright enough to be harmful?
The distance from the earth to geosynchronous orbit is about 23,000 miles. The distance from geosynchronous orbit to the moon is another 200,000 miles. So, no way that one could see satellites from the moon.
You can’t even see the Great Wall of China from the moon, and that’s a heck of a lot larger than satellites!
To give you some idea of scale, from the Moon, the Earth would appear to be about as large as… well, take a golf ball and hold it as far away from your eyes as you can. That’s about how big the Earth would look like. So no, you couldn’t see a rocket launch. You’d barely be able to make out the shape of the continents.
Can you see the lights of major cities? (Say, standing on the dark side during a half-moon phase? Or even during a terrestrial eclipse during a full moon?)
By these numbers, I’d actually think that you could see them a lot of the time.
From Earth, satellites are amongst the brightest objects in the sky: someone at Yahoo! answers opines that they have an apparent magnitude of -1. by the inverse square law, satellites should be only 75 times dimmer from the moon than they are from Earth. You’d have to be 625 times dimmer in order to not be seen from the moon. According to my calculations this means that satellites should look like magnitude 3 or 4 stars from the Moon.
So, in those situations where the Sun is obscured, but the Earth is still visible from the Moon, you’d probably be able to see satellites that are not set in front of the Earth unless there is so much earthlight that it disrupts your low level vision (which I can’t calculate right now.)
I’m pretty sure you’re thinking of low-earth orbit satellites. Geo satellites tend to be around magnitude 10 or so, maybe 5 (or a little better) in good conditions.
Diameter of the Earth: ~12,800 km
Diameter of the Moon: ~3,500
So from the Moon, the Earth will between 3 and 4 times bigger than a full moon does from here. Surely an impressive sight, but it would hardly fill the sky. You wouldn’t be able to distinguish any features that aren’t visible on a globe. The smallest features you can make out with the naked eye when viewing a full moon are on the order of hundreds of kilometers across, so only similar features would be visible on Earth from the Moon. Things like mountains, lakes, forests, deserts etc. Large conurbations like Los Angeles or the Philadelphia-NYC-Boston area might be visible during the day, and imagine many cities would be visible in the dark portion of the Earth. But any structure smaller than tens of miles on a side would be invisible.
As for the second part of your question, I think Iridium flares might be on the verge of being visible from the Moon. Someone else can do the math, but in my head it seems like they’re at least within a couple orders of magnitude of being bright enough. But on second thought, at an altitude of only 500 miles or so they’d always be very close to Earth in the Moon’s sky, which would probably be bright enough to drown them out.
About the same brightness as looking at asphalt on a bright day.
So, nah. Although, you might wish to wear some heavy-duty UV protection.
Ten posts in and no one has bothered to link to aphoto of the Earth from the Moon?
I looked at photos of the Earth from the moon, but they don’t tell me if you’d see a rocket launch. 
Also, that doesn’t look as small as a golf ball as far from my face as I can hold it… But that’s still pretty darn small.
Thanks for your responses, guys. Now I feel kind of dumb for thinking it would be possible to see satellites or rocket launches from the moon… The thing is, if they were visible, it would make for a pretty awesome scene in a fan fiction I’m writing. Oh well.
At least now I know Chell doesn’t go blind at the end of Portal. XD
First thing I thought of was Bugs Bunny and Marvin the Martian.
“A fledgling leaving its nest!”
I don’t recall the context of that particular quote.