"Mild amusement" means to find something amusing or funny, but not to the extent of laughter or strong amusement. It is a light form of enjoyment or entertainment. Full definition
He aims for big laughs, but mostly what he achieves is a fairly constant level of mild amusement. (mountainx.com)
When other playful young dogs tried to engage her she simply backed off and eyed them with mild amusement. (bordercollierescue.org)
Two things stand up best over the years: the power of the battle spectacles, and the strength of certain performances - especially Olivier's fire, Douglas» strength, and Laughton's mild amusement at the foibles of humankind. (rogerebert.com)