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Coincidentally (or not), Matrix, Trinity, Morpheus, 303 and 101 are
all models of music synthesizer (from various manufacturers).
All of the good guys (Morpheus, Trinty, Neo, etc.) in the movie
wear round or oval sunglasses. All of the bad guys (the agents,
Cypher) wear square or rectangular sunglasses.
Nebuchadnezzar was a biblical Babylonian king who was instructed by
god in dreams to destroy the inhabitants of Jerusalem because they
worshipped false prophets.
When Switch says to Neo, "We don't have time for 20 questions," Neo
had just asked approximately his 20th question so far in the
movie.
Check out the room numbers for Trinity and Neo. When the cops bust
in on Trinity in the opening scene the number is 303 ("trinity," 3)
and since Neo is The One the number of his apartment is 101.