But that I am confused about that last part because "Passed [month and year] - awaiting registration" is almost exactly what I currently have on my resume. Why is that wrong?
It's not wrong per se. It just doesn't position you in the best light.
(a) In some instances, your resume will first be screened by a software filter, searching for the magic words "Registered Patent Agent, USPTO Registration No. XX,XXX". In which case, the filter will direct your resume to the trash bin.
(b) OK, assume there is no software filter and your resume is screened by a human reviewer. In many instances, the reviewer will skim your resume for ~ 30 sec and sort it into one of three bins: "yes" (worthy of further consideration), "no" (trash), and "maybe" (requires special handling). Of course, you want your resume to be directed to the "yes" bin. But, since you do not have a registration number, it will likely end up at best in the "maybe" bin, even if your credentials are otherwise a good match to the firm's needs. If the "yes" bin is sufficiently populated, however, the "maybe" bin gets folded into the trash bin. [Of course, you could luck out, and the reviewer thinks "I've never heard of anyone being rejected because of a negative comment", so it's a "yes".]
(c) So you wait, haven't had a nibble, and you eventually get your registration number. You update your resume and send it out again to the same firms (as well as others). If it hits a previous reviewer, perhaps he's forgotten about your first resume, and gives your second resume a fresh look. But perhaps there's a subconscious memory and a hidden bias that he passed you over the first time for some reason.