All those "mistakes", to put it kindly, stain the public image of our association AND the hospital.

stain 是动词，意思是"弄脏、玷污"，常用于比喻名誉或形象受损的情况。在句中 stain 表示这些错误行为给协会和医院的公众形象带来了负面影响，就像污渍玷污了干净的东西一样。