In the final fight scene between Agent Smith and Neo, Agent Smith punches Neo in the chest, and Neo vomits blood. He still has quite alot of blood in his mouth when he wipes it on his hand. However, when you look, Neo has no blood on his hands, they're completely clean!
Yuppers, it's the "believing thing". Notice also how Morpheus looked when he broke free from his chains, and then compare with how he looked on the rooftop. He "freed his mind", and in doing so "believed away" the blood and bruises. Neo must have done the same. Wounds heal quickly in the dream world...
Guys, I think the answer is much simpler than that- Neo wiped the blood with the part of his hand around the thumb, in the next bit where he beckons Agent Smith towards him, that part of the hand is in the shade and you can't see whether it has blood on it or not.
It is a dream world....his mind creates a self image. There seems to be no bruises anywhere...even the jump. Thats nothing. There is a small scene on the roof where Neo is wounded. There is something wrong with his shoulder wound....it looks like plastic cap under the shirt. It is dull shiny bright red not a dark red.
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