While Zeus certainly makes things difficult for Odysseus after the Trojan War, it might be better to consider what Poseidon, god of the sea, does to Odysseus. While Zeus is often less than fond of the wily king of Ithaca, he doesn't hate him nearly as much as Poseidon does (although he also doesn't like him as much Athena, Odysseus' most avid fan on Mt. Olympus).
In a nutshell, Zeus does two main things to Odysseus after the cunning warrior leaves Troy. He destroys Odysseus' ships after the king's men blasphemously feast on Helios' sacred cattle, and then he allows Odysseus to fall under the spell of Circe and be trapped on Ogygia for seven years. Zeus committed this latter action to appease Poseidon, Odysseus' primary antagonist (other than the ill-fated suitors, of course). Poseidon is mostly furious with Odysseus because the king of Ithaca blinded Poseidon's son, the monstrous Cyclops Polyphemus. After this incident, Poseidon makes it his priority to hassle Odysseus and make his return journey as difficult as possible. Thus, while Zeus often harries Odysseus, he often does so on the request of Poseidon, Odysseus' real adversary.