Last night, I accidentally dipped my finger into a bowl of milk I picked up. I had eaten meat for dinner a few hours prior and I’m not my sure if I washed my hands afterwards (I actually touched meat at dinner). Are there any kashrut concerns with the bowl and spoon that was inside? Everything was cold. I assume I can just wash it with soap?
Correct, there is no need for you to do anything special about this. In all probability, there was nothing on your finger, and even if there was, it was botil. Therefore the is no concern here.