Although controversial, George's act of euthanasia was for the best. George's act was justified by the lynching mob ready to hang Lennie, the probability of the same scene being repeated, and the danger that Lennie presents.
Because of Lennie's actions, George and he are unable to hold jobs for a long time or have a permanent job. Everywhere they go, Lennie gets them into trouble and they are forced to leave. In Weed, they are forced to hide in an irrigation ditch all day and night, so they will not be hung. This scene has happened in the past, and it will inevitably happen in the future.
The question arises of how many more people will die or be hurt at Lennie's hands. Everywhere that Lennie goes he endangers others. Although his intentions are good, he is too strong and too ignorant of his own strength. He does not realize that he has done a "bad thing" until it is too late to fix it. Innocent people should not have to die because Lennie can't understand that he hurts them.
At the end of the novel, there is a group of people that are ready to kill Lennie. Lennie would die scared and unhappily. At best he would be locked away in a "booby hatch." Either way, he would die miserably. By shooting him, George offers him the most merciful and least painful death that Lennie could have; he dies happy.
Lennie is not, by definition, a "bad" person; he does not intend to harm anyone. Nevertheless, people do die at his hands. By offering him a quick and painless death, George does the right thing. .