There was a time when ministers would hole up in their studies, surrounded by commentaries and occasionally distracted by a phone call.
Though I am not a pastor, I suspect that today's minister has a few commentaries or other pertinent thematic texts on the book shelf but that the primary tool is The Internet.
I have only heard of anechdotal evidence about pastors who are tempted to check out websites that are not particularly conducive to theological exploration. Left alone in their studies or church offices for hours on end, the temptation to check out pornographic sites does exist. A few pastors honestly and sheepishly admit to that lure.
While this question and this discussion could properly belong under the Pastors section, the need to address this question may very well fall into the lap of a classis. While I don't imagine a candid discussion on 'pornography in the study' taking place at classis, there may be room for the Classis Ministry Committee or some similar counterpart to provide a support group for those pastors and church leaders within classis who struggle with that temptation.
It will undoubtedly require one incredibly strong minister to 'come out' and admit that he/she is dealing with pornography and "who wants to join me in a support group".
I don't know of any congregation, classis or synod that has acknowledged this new, hidden reality.