Amongst the commanders in Attack On Titan, Erwin Smith starts out as one of the best. Erwin, 13th Commander of the Survey Corps, created the Long-Distance Enemy Scouting Formation that led to the trapping of the Female Titan. Unfortunately, this feat wasn't enough to make up for the mistakes he made leading up to losing his father, and those that came after.
Erwin had a genuine goal of making humanity the dominant species once again but he dedicated himself to these ideals at the sacrifice of his men. Like many of the leaders in AoT, he was willing to sacrifice his own humanity for the sake of it all, emotions and compassion included.
"Scream"
Erwin led his soldiers into battle in an attempt to retrieve Eren from Reiner, the Armored Titan, and Bertholdt. Ymir had a plan but instead, Erwin interjected himself, lost his arm and a lot of soldiers while letting Reiner get farther with Eren in the process.
While Mikasa rescues Eren, as usual, Erwin sits by wallowing and listening to his own scouts die around him.
Confessing To Nile
Nile Dok was the Military Police Brigade commander when he and Erwin were closer friends. Even though they grew apart, Erwin felt comfortable enough to meet with Nile and tell him of his gamble to retake Wall Maria with Eren's Titan abilities.
This backfired because of Nile's logical mindset. Nile would rather have Eren executed since a civil war between citizens of the Walls was too risky. This revelation to the government put Erwin on trial, put Eren's life at risk, and put an even bigger gap in Erwin and Nile's friendship.
Lying To Levi
Topping off the end of Season 2 and following after the loss of his arm and many of his men, Erwin is recovering and hears Connie's theory that the Titans of their most recent battle were actually the human citizens of Ragako. With this news, Erwin smiled knowing that he was closer to his truth. Levi was surprised to see him smile.
He mentions that the Walls are barring them from the truth and they will break through them with time. Levi, and even fans, thought he meant figuring out Titans, their purpose, and how to get humanity back on top, but he was talking about avenging his father and continuing their personal mission.
Battle of Shiganshina
The Survey Corps planned to locate and investigate Grisha Yeager's basement and Erwin rejected the idea of him staying back since he had recently lost his arm and could be lost in this battle.
During a feast, Erwin revealed they possessed the Titan serum and would give it to the wounded soldiers to turn them into mindless Titans so they could continue fighting. For someone who wants humanity to live on and dominate, this is a strategic plan but a contradictory one.
The Female Titan
While the mission was a temporary success in capturing the Female Titan, later revealed to be Annie Leonhart, it was at the sacrifice of Erwin's troops.
Due to his order to continue pushing into the forest, he lost one whole flank of soldiers but kept going. Even his troops were surprised by this order. He continues to make bad calls on the return to Karanes and is summoned to the capital.
Wall Maria
Erwin's motivation for saving humanity was based on his passion for proving his father's theory that humans did this to themselves by being greedy and that there is life beyond what the government has created for them.
This blocked his judgment enough to the point where instead of retaking Wall Maria when the territory was lost, he pushed through to try and find the secrets in Eren's basement and was unsuccessful.
"Midnight Sun"
Erwin has caused so much loss for his soldiers that Floch even considered killing him when he found him wounded during the battle with the Beast Titan.
But instead, Floch brought him back to Levi for the Titan serum so he could suffer through more loss and guilt. To some of the soldiers, Erwin "is a devil." In the end, he died because of the mercy of Levi but not outwardly acknowledging that he was remorseful for all the loss he caused is what made many of his gambles, mistakes.
His Father's Death
This is the most unfortunate of Erwin's mistake and he was a child at the time so it can't be held against him. The guilt he holds close to his heart and losing his father is what drives Erwin's personal mission.
At one point, he repeated Clause Six of the Charter of Humanity, "One must never prioritize their own gain over humanity's survival." While he constantly is in search of new ways to help humanity persevere, he also always had ulterior motives because of the guilt of causing his father's death by talking about his government theory.