The potted meat is referenced in a newspaper ad. It suggests that a home without the potted meat is incomplete. But with it, a home is "an abode of bliss." The meat is symbolic of how Bloom feels about himself, his home, and his relationship with Molly. Bloom worries that he is not the head and leader of an abode of bliss, but rather a secondary figure in an incomplete home. That suspicion is driven home when he finds evidence of potted meat in his own bed left over from his wife's tryst with Boylan.
The horse race is symbolic foreshadowing of Bloom's eventual success to win Molly back from Boylan. The horse "Throwaway" was not supposed to win. Very long odds against it, but it does end up beating the favorite "Sceptre." Just as Bloom beats the publicly favored Boylan.
Bloom has Irish heritage. Potatoes are often associated with Ireland. It's symbolic of that past. A reader could think that the potato is symbolic of Bloom's fears. He has worries about his fertility and future family. The potato is shriveled and old. Bloom's fertility is possibly shriveled and old. This one has always seemed a bit of a stretch for me.
The hat is pretty easy because Stephen intentionally tries to make it a symbol. He calls it his "Hamlet" hat, and he sells it as such by being such a dark and brooding character. The black clothes and being in mourning help too.