One piece of symbolism in the novel is lightness and darkness. Joyce sort of flips the standard symbolism on its head, though. Normally, black and darkness signal to an audience evil and "bad guys." Think Darth Vader and Star Wars. The motif is all over the place in Hollywood. Light and light colors then symbolize goodness and heroism. That's why Luke Skywalker is generally wearing white or light colors, and why Darth Vader asks him to "join the dark side." "Ulysses" flips the motif. Dark colors are worn by the good guys and the antagonists typically wear light colors and have bright and vibrant personalities.
A universal message in the novel is the importance of considering multiple viewpoints before making any kind of judgment. Joyce stresses this by telling the story through multiple viewpoints and the concept of parallax. Parallax is an astronomy tool used to measure the distances to stars and galaxies. It uses the apparent shift in star position that results as the Earth moves from one side of its orbit to the other side (6 months later). If you hold your thumb up in front of your face and alternate which eye is open while looking at it, your thumb appears to wiggle back and forth. The amount of visible shift can be used to determine how far away your thumb is (or a star). Different viewpoint, different perspective.
Joyce constantly keeps the reader re-evaluating judgments by changing the perspective that the reader hears from. A reader may think about a certain character in a particular way until that reader "hears" it from that character's perspective.
Atticus Finch told Scout the same thing in "To Kill a Mockingbird" when he told her that to truly understand someone it's important to walk around in their skin for a bit.
"First of all," he said, "if you can learn a simple trick, Scout, you'll get along a lot better with all kinds of folks. You never really understand a person until you consider things from his point of view . . . until you climb into his skin and walk around in it."
I'd say that idea is a pretty important universal message, if both Joyce and Lee wrote about it in their novels. It could be argued that both books are among the most influential of the 20th century.