Robin Hanson sometimes complains that when he tries to argue that conclusion X follows from reasonable-sounding premises Y, his colleagues disagree with X while declining to say which premise Y they think is false, or pointing out which step of the reasoning seems like an invalid implication.

I parsed this as "...his colleagues disagree with X while declining ... or while pointing out which step of the reasoning seems like an invalid implication", which is the opposite of what you meant.

I think the correct syntax here is "...his colleagues disagree with X while declining to say which premise..., or to point out which step...", which links the two infinitives "to say" and "to point out" to the verb "declining". ETA: The current edit works too.