They are interagating Morpheus in the government building, and you can clearly see that around his nostril area is bloody. But after Trinity drops him off on the roof to go meet Neo his nose is completely fine, with no blood. So how did Morpheus have time to wipe it off if both of his hands were busy?
You're noticing the blood on his nose disappearing, but not the obvious of his shot leg, which in the next scene appears to be completely mended. This isn't a slip up, it was intended to emphasise Morpheus's strength over the Matrix, and to imply from his statement of "The mind makes it real" that the mind can also realise the truth and overcome the illusion.
did you guys notice that when Neo and Trinity blow up the lobby the the fire SPRINKLERS turned on?
sprinklers=water
water=washing
washing=no more blood!