Which cases were which?
"In reply I have to state that if you will furnish me with the names of one or two persons whose arrest would be likely to produce a proper effect upon the course of that paper I will communicate a decision upon the subject."
What was that decision? Was anyone actually arrested?
Not that I could find. Apparently excluding the National Zeitung from the mails had the effect of shutting the paper down so the editors weren't arrested. It ceased publication shortly after being excluded from the mails.
POST-OFFICE DEPARTMENT, September 14, 1861.
Honorable WILLIAM H. SEWARD, Secretary of State.
SIR: I have the honor to acknowledge the receipt of your notes of the 12th and 14th instant and to inform you that on the day of the receipt of your first note an order was made excluding the National Zeitung from the mails and the postmaster of New York instructed to execute the order. The circulation through the mails of the Staats Zeitung has not been prohibited.
I am, very respectfully, your obedient servant,
JOHN A. KASSSON,
Acting Postmaster-General
I take it that this is the sort of thing you are looking for:
WASHINGTON, September 2, 1861.
ROBERT MURRAY, U. S. Marshal:
Arrest the editor of the Greenport Republican Watchman and send him to Fort Lafayette and deliver him into the custody of Colonel Martin Burke. If he has left home for Syracuse arrest him anywhere on the road where he can be found.
WILLIAM H. SEWARD.
[you] Which cases were which?
Too lazy to look in the link I provided? Here is what they cited:
On February 23, 1863, the Davenport Daily Gazette in Iowa reported that some seventy-five convalescent soldiers from a near-by military hospital entered the office of the Keokuk, Iowa Constitution, wrecked the presses and dumped the type out the window. (65) In the spring of 1863, the Crisis and the Marietta, Ohio Republican, a Democratic paper, suffered damages at the hands of a mob of soldiers. (66) The next year a number of other newspapers in the Midwest, including the Mahoning, Ohio Sentinel, Lancaster, Ohio Eagle, Dayton Empire, Fremont Messenger, and the Chester, Illinois Picket Guard experienced similar visitations. (67)
Here is confirmation from another site that the Picket Guard was destroyed by soldiers:
In 1864 soldiers stationed in Cairo marched a short distance from their camp to destroy the press and offices of the Chester Picket Guard, a persistent critic of the war and administration.
It is unclear from the information I found what kinds of pro-Union mobs destroyed the Easton paper and tarred and feathered the Massachusetts editor. I posted the exact wording about those incidents that I found on the web.
I also posted the exact wording I found about the Bloomington Times -- that was listed as a pro-Union mob. I also quoted PeaRidge's post that stated a mob of soldiers demolished the offices of the Democratic Standard in DC and a Unionist mob destroyed the printing facilities of the Bangor Democrat.
Apparently it wasn't very safe to say anything against Lincoln in the North.