When the kohen does an avodah shelo l'shma and the baal must bring another, who pays for the second animal?
This is a case of היזק שאינו ניכר unnoticeable damages. According to Torah law one is exempt from payment in such cases, but the Sages instituted that one who damages someone else's property in this way on purpose must pay. If it was an accident though then the damager remains exempt from payment. (Gittin 5:4, Rambam Mazik 7:1-4, Shulchan Arukh CM 385:1)