First, go to the section in the movie where Morpheus and the others take Neo(Keanu),back to what he thinks is the 'real world'. They are all in the car as Neo looks out the window. Neo observes the place where he used to eat 'noodles'.

If you look closely at his hair, you can see it's a wig, as he had his head shaved for the movie, scenes are not in order as we all know. The next scene of Neo from then on is Neo's real hair.

The key to noticing the difference is the sideburns are a completely different shape.