And apparently our stellar Senator Durbin has now realized this himself, as he has changed the wording on his YouTube channel after the fact. Look at the before screenshot campaign wording on the channel title "Dick Durbin for Senate" and the page says "All the latest videos from Senator Dick Durbin's election campaign". The url is the campaign website, not the official one, and you can see the U.S. Senate seal superimposed on the frozen video screen.Now look at the YouTube link. It says "Senator Dick Durbin" and "All the latest videos from Senator Dick Durbin". The campaign url address is still there and you can still see the seal.
Judge for yourself.
Following are related links and excerpts from the Senate ethics manual. The Senate Ethics Manual specifically forbids the use of the Senate seal for campaign use:
SENATE ETHICS MANUAL, CHAPTER 6, QUICK REFERENCE TO FREQUENTLY ASKED CAMPAIGN-RELATED QUESTIONS, PAGE 151 - http://ethics.senate.gov
•Great Seal, Senate Seal, on campaign documents—The Seal of the U.S. Senate is in the custody of the Secretary of the Senate and generally is used only to authenticate official Senate documents (an alternative, non-official seal has been authorized for use by Senate offices and on items sold in the Senate gift shop). Both the Senate Seal and the Great Seal of the United States (depicting an eagle clutching items in its talons) are protected by 18 U.S.C. 713, a criminal statute. That provision is intended to restrict the knowing display of the Senate Seal or the Great Seal or any facsimile thereof in any manner reasonably calculated to convey a false impression of sponsorship or approval by the Government of the United States. Thus, commercial use, personal use, or campaign use of these seals would be improper. (See section on the Senate and Great Seal in Chapter 7 and 18 U.S.C. 713 in Appendix D). If a Member’s campaign wants to use a symbol of government on its campaign stationery, a depiction of the Capitol dome would be appropriate.
(The Senate Ethics Manual continues):
SENATE ETHICS MANUAL, CHAPTER 7, USE OF THE GREAT SEAL AND THE SENATE SEAL, PAGE 172 - http://ethics.senate.gov
The Seal of the U.S. Senate is in the custody of the Secretary of the Senate and is used only to authenticate official Senate documents. With the written permission of the Secretary, images of the Seal may be reproduced in educational publications for educational purposes. In addition to the official Senate Seal, the Secretary has also authorized an alternative, non-official Senate Seal. This alternative seal, which features an eagle clutching arrows and an olive branch in its talons, surrounded by the words ‘‘United States Senate,’’ is commonly used by Senate offices and is often displayed on items sold in the Senate Gift Shop. Even more commonly seen perhaps is the Great Seal of the United States (also depicting an eagle clutching arrows and an olive branch in its claws). Both the Senate Seal and the Great Seal are protected by 18 U.S.C. 713, a criminal statute. That provision is intended to restrict the knowing display of the Senate Seal or the Great Seal or any facsimile thereof in any manner reasonably calculated to convey a false impression of sponsorship or approval by the Government of the United States. While the interpretation of this statute is a matter for the Department of Justice, it appears that in most cases use of the Senate Seal or the Great Seal for normal official Senate business would be appropriate; by contrast, commercial use, personal use or campaign use would be improper. Although the Committee has not issued an Interpretative Ruling on the use of the Senate Seal (official or alternative) or the Great Seal, many of the practical restrictions on their use are similar to the restrictions on the use of the ‘‘United States Senate’’ letterhead. See, for example, the discussion on use of the Senate letterhead above, which states that the letterhead should not be used for campaign or other fundraising purposes.
(Also, in the event that the video was produced with official resources, the Ethics manual makes it clear that it should not be used for campaign or political activities):
SENATE ETHICS MANUAL, CHAPTER 6, CAMPAIGN USE OF OFFICIAL RESOURCES, PAGE 153 - http://ethics.senate.gov
Official resources may only be used for official purposes. This principle derives in large part from 31 U.S.C. § 1301(a), providing that official funds are to be used only for the purposes for which appropriated, as well as from statutory authorizations for allowances. 418 It is thus inappropriate to use any official resources to conduct campaign or political activities.
UPDATE: Dan Curry, Reverse Spin has some more insight on this.