Once Light gets ahold of the Death Note and discovers its abilities, he immediately gets to work ridding the world of criminals he deems unworthy of life. This initial action sets Light up for failure from the beginning as, though he takes the time to familiarize himself with the Death Note's rules, he decides to make a calling card out of its default killing method, making his murders easy to recognize. Soon, criminals across the globe were all mysteriously dying of inexplicable heart attacks, making detective L realize that someone was causing the heart attacks without being present. Had Light manipulated various causes of death that were more natural or believable, L may not have suspected foul play in the first place.
Light's god complex gets the better of him when he wants the world to know about Kira. He uses this Kira persona as a threat to criminals and a reassurance to the public that he will make the world a better place, but he could've accomplished such a feat much easier if the world hadn't known about him at all. Light's arrogance makes him fall for L's initial trap by killing off Lind Tailor, a criminal masquerading as L on live TV. Not only does this confirm that Kira can kill anyone from afar, but it reveals the limitation that Kira needs the victim's name and face to target them. L also broadcasts this exclusively in the Kanto region, revealing Kira's location by significantly narrowing down his search to this single geographic area.
While outing his own existence and geographic region were fatal mistakes from the beginning, Light makes several more blunders that could've been prevented if he hadn't let his ego make all the decisions. After Light reads his father's computer and sees that the police noted that Kira kills at a specific time, he immediately starts changing the time of death for his victims. This sudden change in course makes L realize that Kira must be close to a high-ranking officer and, after researching the officer's families, L comes across Light and labels him a suspect. This later leads to Light's encounter with an FBI officer named Raye Penber, who reveals to Light that he's a suspect. Instead of keeping Raye alive so he can advocate for Light's innocence, Light unnecessarily kills him and makes himself a bigger target.
Light nearly compensates for his prior blunders after helping his father's task force search for Kira. Despite being under L's suspicion and interrogation, Light masterfully evades the authorities and convinces others on the task force that he isn't Kira. After teaming up with Misa and getting a second Death Note in play, he's able to feign innocence while criminals continue to die. Working with Misa and Rem was one of Light's smartest moves, as it ultimately leads to L's death. However, L's death only confirms Light's belief that he's untouchable. This false confidence leads to his ultimate mistake -- underestimating L's successors.
With L out of the picture, Light barely flinches at the introduction of his replacements: Mello and Near. These successors immediately suspect that the new L is also Kira, and Light falls into suspicion once again by being exactly that. Light's carelessness causes his own task force to suspect him yet, he doesn't kill Aizawa, who was directly working against him. When Mello later kidnaps his sister, Light makes several mistakes, like trusting his father to kill Mello instead of doing it himself. While Mello eventually sacrifices himself to aid Near's investigation, his death forces Teru Mikami to reveal the location of the real Death Note.
Light blindly trusting Mikami to be an intelligent and effective partner in crime (despite barely knowing him) was a fatal mistake that directly leads to his death. Since Mikami acted on his own and tried to kill Takada when she was kidnapped by Mello, Near is able to trace his whereabouts to the real Death Note and switch it with a fake one -- without Light knowing. This leaves Light powerless at the warehouse after arrogantly confessing to everyone that he's Kira and proclaiming his victory.
While Light is a notable genius who made impressive tactical moves that helped him evade the authorities for a long time -- despite always being under suspicion -- his collection of failures far outweigh his successes. Despite besting and killing his main adversary, L, Light wasn't able to overcome the detective's clever successors, who he fatally unerestimated. Given this antihero's string of errors and impulsive decisions, Light's inflated ego and ultimate death prove that he was never as smart as he and the audience gave him credit for.
