I think the most interesting part of this is the cast of characters in the room: The president is talking to Chief of Staff Bob Haldeman again -- but also Attorney General John Mitchell, National Security Advisor Henry Kissinger (again), Press Secretary Ron Ziegler, and Secretary of Defense Mel Laird. Needless to say, none of them seem to have pointed out that the president was proposing crimes, or even quietly resigned.
(By the way, I'll try to be consistent here; regular ellipses are from the transcript provided in Stanley Kutler, ed., Abuse of Power; I'm using bracketed ellipsese (i.e. [...]) when I'm skipping over things. Also, I'll provide a link if it's from a web source, usually the Miller Center. Emphasis here from Kutler).
President Richard Nixon: They [Brookings] have lot of material...I want Brookings, I want them just to break in and take it out. Do you understand?
Haldeman: Yeah. But you have to have somebody to do it.
President Nixon: That's what I'm talking about. Don't discuss it here. You talk to [E. Howard] Hunt. I want the break-in. Hell, they do that. You're to break into the place, rifle the files, and bring them in.
Haldeman: I don't have any problem with breaking in. It's a Defense Department approved security --
President Nixon: Just go in and take it. Go in around 8:00 or 9:00 o'clock.
Haldeman: Make an inspection of the safe.
President Nixon: That's right. You go in to inspect the safe. I mean, clean it up.
Part of what's going on here that's terribly important is that the FBI isn't willing to do the things that the president wants; see this conversation between President Nixon and Attorney General Mitchell the previous day. As I've written, one way to understand Watergate is through the general notion of the weakness, not the strength, of the presidency. Nixon is supposedly at the top of the executive branch, but he can't get people in the various departments and agencies to do what he wants because they generally won't follow orders from the president -- that's not actually how the presidency works. It's not just illegal or unethical stuff; Nixon and his National Security Advisor Kissinger are busy running foreign policy without letting the State Department know what they're doing.So that's what's going on here: since the FBI won't do what the president wants, he's going to do it himself. That is, he's going to do it from within the White House. And in this one, we get the name of one of the people who is going to do what the FBI won't do, E. Howard Hunt.