Logan saving an enemy soldier and complete stranger from the nuclear explosion in Nagasaki. On top of that, said stranger is an officer of the base where Logan's being held as a POW.
Wolverine putting the bear out of its misery and tracking down the hunter who caused it harm
After Mariko's father tried to kill her and she had to kill her grandfather before he killed Logan Mariko tells Yukio before the latter departs with Logan that she is her only family. Yukio in turn calls her 'sister'.
Logan gently bringing Yukio around after Shingen knocked her out.
Also when he saves her from Shingen, saying "Don't hurt my friends."
Mild example, but the look Mariko gives Logan as he's helping to clear the tree. It reads as equal parts admiration, gratitude and blossoming attraction.
After being his literal Nightmare Fuel for the bulk of the film, Logan finally being able to let go of Jean. The closure of finally being able to forgive himself for stopping her rampage is not only one of the few moments we ever see Logan at peace, but it also comes across as something the real Jean would have wanted for him.