So, I'm trying to check us in, we're a total of three pax.

When I start the process, I click on the "select all" button, and all three names get the green checkmark.

Next screen, I'm listed first, I confirm my pax info, provide an emergency contact, and click "verify".

Next pax, same deal, but when I click "verify", it thinks about it for a while, and when pax 3 info shows up, only pax 1 and 3 are listed.

I tried a couple of different browsers, same deal.

I went to back to the beginning, and clicked through until I got to the seat selection (without going the check-in route) and all three pax show, with the seats I've had all along, etc.

Is anyone else having problems checking in tonight?

Gonna reach out to @DeltaAssist next.

Meh.

"Must verify id, need to check in at the airport"

All three of us had no problems checking in two weeks ago when we started the trip. The kids even got TSA precheck.

Will not try to understand.

International flight? Might be the dreaded SSSSS.

Intl flights are ID/Travel Doc verified by DL staff before the check in process is complete.
One would see DOCS-OK printed or stamped on their BP once this verification is done.

Just within the last few days I did OLCI successfully for an international DL flight. At the lounge, I showed my passport and the agent stamped DOCS OK on the boarding passes that I had printed in my office.

Has the OP tried doing OLCI for one at a time?