Takemichi learns several key lessons from his failures and mistakes throughout the series "Tokyo Revengers." Some of the important lessons he learns include the value of taking responsibility for his actions, the importance of standing up for what he believes in, the power of friendship and loyalty, the impact of his decisions on others, and the significance of never giving up, no matter how challenging the circumstances may be. Takemichi's journey is marked by growth and self-discovery as he navigates through his past mistakes and strives to create a better future for himself and those around him.