What type of distribution should binding affinities fit?
P-values reflect how well the data fits some background model. This background model should reflect some assumptions you make about the data. What assumptions do you think would be reasonable in this case? For example, do you assume high values are more likely to be incorrect?

Throwing away outliers like kmm suggested is probably not a good idea, because it means you will remove $K_i$ values which are very high or very low. It is not clear there is much biological justification for that, since we know some $K_i$s can be low and some can be high, but it doesn't tell us they are wrong.

The bottom line is that without making some assumption about what the values should look like, you can't identify what incorrect values look like.