Zeus, as the King of the Gods, is very proud, commanding and has an extremely high amount of self-respect, almost to the point of condescension and narcissism. He demands respect and precedence from mortals, demigods, and the other gods. One of the many examples of this is in The Lightning Thief when he was slightly irritated because Percy acknowledged Poseidon before himself.
Despite being the god of honor and justice and demanding high standards from others, Zeus does not always provide the best moral example. He is, at times, extremely paranoid, as well as hypocritical, self-centered and easily insulted. He forced the oath to have no half-blood children on his brothers going so far as to try and murder the children of Hades and claim Poseidon fathering Percy as a severe crime, yet Zeus broke this oath himself and played favorites by trying to save Thalia while forcing her to endure the consequences of his broken oath. He can also be incredibly jealous when it comes to his wife Hera as depicted when he punished a mortal who once tried to court Hera. Yet he has become infamous for breaking his marriage vows to her time and again reflecting his lustful and libidinous nature. His rampant unfaithfulness to his wife Hera is a very prominent theme in Greco-Roman myths, and he often places his mistresses and even his own children in dangerous situations all in the attempt to hide his affairs.
If he imagines that he is being plotted against or insulted, he can be very unforgiving. He often allows his negative traits to override his better judgment. His decisions are not always based on justice, but rather his personal whims and what he sees as best for himself, rather than the greater good. Zeus is, in some ways lustful for power. It is evident in his title as King of the Gods and his fear of his own brothers betraying or dethroning him.
Zeus has a tendency to hold grudges. He has a very strong and lasting distrust of Poseidon as he falsely believes the latter had once attempted to overthrow the former from his throne (when really all Poseidon wanted was for Zeus to be a better ruler). Zeus instantly blames Poseidon for anything that the latter could be guilty of in the barest despite having no evidence and all facts pointing to the contrary. For example, he immediately blamed Poseidon for stealing his weapon without even understanding the entire situation. Later, he blames Apollo for hastening the second Gigantomachy and continues to distrust him for participating in the attempted overthrow and for once killing several of the Elder Cyclopes to avenge the death of his son.
Zeus hates damage to his self-image and tries to assign blame to others to avoid making himself look bad. He blames Apollo and Hera for the second Gigantomachy and the conflicts between the Greek and Roman demigods since Apollo assigned a new oracle who spoke the Prophecy of Seven and Hera took it upon herself to interpret it. This ignores the facts that Apollo has little direct control or understanding of the prophecies made by the oracle and that the giants were already rising. If Hera had not acted it would have been too late to do anything. Also Zeus was being manipulated by Khione.
Zeus is noted to often be quite unreasonable especially if he has been proven wrong or made a fool of. He get angry, try to assign blame elsewhere, and takes any attempts to reason with him as challenges to his authority. The only thing one can do is wait for him to calm down and try to reason with him later.
Zeus' several flaws often get in the way of him being a good king. His refusal to change his decision when he is wrong, decides to put himself before the other gods, or even admit a problem actually exists has put both Olympus and the world in danger numerous times. Hence, it has been noted that it is actually Hera who holds Olympus together and without her the gods would quickly implode.
Despite being the Ruler of the Universe, Zeus is also prone to making huge tactical blunders, which throws Olympus's safety into jeopardy. He didn't bother to maintain a standing army to defend Olympus, throwing the responsibility on Percy, Annabeth and Chiron. Despite repeated warnings, he gathered all the gods to fight Typhon, when the real threat was Kronos. Zeus didn't bother to take immediate action against the rising Titans, much to Percy's dismay. Subsequently he didn't bother to stop the Giants immediately either. Instead he made it worse by cutting off communication with the demigods.
Zeus apparently has a flair for dramatic exits and is a quite a show-off, a trait Poseidon pointed out to Percy, saying that Zeus would have done well as the god of theater.
Despite his several flaws, Zeus does have a somewhat respectable side. He does love his children, but cannot show as much love as the other gods do, as he is the leader and must set an example. It also cannot seem that he is merely choosing favorites. Despite this, he often does play favorites especially his daughters, such as sparing Thalia while insisting Percy's birth is a crime in itself. He also favors Artemis over Apollo, despite both disobeying him at times, and Artemis has confirmed that Zeus has never been able to be angry with her long, since she has the ability to charm him into forgiving her and Athena since she wasn't punished in the first attempt to defeat him. Zeus is still quick to turn on his children if he feels they have somehow insulted him or challenged his authority.
Although Zeus is short tempered and vengeful, he is also capable of sympathy for those that have suffered the same injustices that he and the other gods suffered in their lives. A clear example of this can be found in The Titan's Curse, where he was the most willing to kill the Ophiotaurus due to the risk that it posed to the gods. Percy Jackson, however, pointed out that what they wish to do was the same thing that Kronos tried to do with them in the past, and Zeus was the first god to acknowledge the injustice and reconsider his decision.
Despite his usually strict, serious, and prim demeanor, in Percy Jackson's Greek Gods, Zeus is revealed to have a fun and entertaining side as well (which he rarely demonstrates, however), as well as quite the sense of humor, thanks to his knowledge of many outrageously hilarious Satyr jokes.