I'm pretty amazed that Clark is holding it together. I think part of what's helping him is the fact he's wearing the suit. He has programed himself that while in the suit he acts a certain way, and is able to push down his emotions better than when he's being himself (Clark).
I thought the inner debate on whether or not he was invading all these people's privacy was an interesting one. I personally would have thought he'd go with the though process that since he's not "really" looking at these people, merely observing the environs in which they're located, it wasn't "really" an invasion of privacy, since he didn't -- in fact -- care a wit about them. But, you're probably right, he'd find such thinking a compromise of his morals (and one of the reasons, I've always found alt-Clark much easier a character to work with than canon Clark, because of this blurring of the lines would be acceptible, I think, to him).
At first when he landed at the Daily Planet and went to talk to Jimmy, I thought he was going to reveal to Jimmy his secret identity. And, I was like
Are you going to let us be privy to Perry's "push" on Superman?
I'm glad Superman was honest with Bill Henderson about the person he wished the policeman to search for. I could see Henderson balking without that information. Did he really think that Lois and Clark were playing a joke on Superman? Really? That would be a cruel joke indeed.
I know that Clark can't scan the underground lead-lined areas, but he's acting like he can't go near them because they would hurt him (as if lead were Superman's new Kryptonite). I know that's not what he means, but that's what it sounds like when he says things like:
I'm conducting a search for a missing person and there are places that I can't look because they are lead lined.
He IS, in fact, able to look (as well as MPD) but he cannot look quickly and it would slow down his progress in searching for Lois elsewhere. Unless, of course, he means that because these locales are lead-lined, it's possible that the man who took Lois <<cough, cough>> Tempus <<cough>> might have hidden Kryptonite there to slow him down, or trap / kill him.
I'm sure that Bill accepts Superman's explanation on why Clark shouldn't be a suspect, but I'm less sure about Lucy, Ellen, and Sam's reaction.