The International Space Station is orbiting 240 miles above the Earth. You can see the bright blue background just like what was seen through the windows of the Apollo capsule in the faked footage. Additionally, our current spaceshuttles can only go 200-400 miles into orbit.
The trip to the Moon is 239,000 miles one way. Are we really supposed to believe they had better manned spaceflight technology in the 1960’s than currently? Given this bit of perspective, we realize that we are not even remotely close to sending (or having been able to have sent) men to the Moon technologically speaking!