Well I did try again to dig in to the paper, but finally realised that there is not enough detail in the paper to allow me to decide in principle whether there may be a real anomalous effect, or not.
Some very rough notes below... in no particular order.
My suspicion is that there may be a problem in the experiment design which allows some information to pass between the 3 experimenters, such that the target reading is unconsciously signalled to the sitter. This would unconsciously bias the sitters scoring on statements that are more open to interpretation. Results from separate sitter scoring on the more factual statements about the deceased was not significant. Indicating that where interpretation by the sitter is reduced, the effect drops away, which would seem to support the idea of unconscious signalling to the sitter.
Without more practical information about how the readings were passed between the experimenters it wasn't possible for me to untangle the experiment.
I do get concerned when people work together for long periods of time with the same people, and claim they have found anomalous transfer of information. This does remind me a little of the recent Diane Powell claims.
In any case, the experiments design prevents us from checking whether the information provided by mediums about the deceased was accurate. The judge of accuracy is left to the sitters alone. This also suggests that the results obtained are due to something at the sitter end of the experiment, and probably have nothing to do with the mediums.
It seems to me that the sitters are merely being asked to make a yes/no choice about two bits of information which are wide open to interpretation. The results are then caused by some bias, due to an effect between the experimenter and sitter, and probably has little to do with the accuracy of the information.
Whether this effect is anomalous remains unclear, but it doesn't appear to be related to the medium at all. If it were anomalous it seems more related to the experimenter effect, the UBC Ouija board study, hypnotism, etc. That is an effect caused by one person on another.