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This part doesn't make sense to me. C-3PO says it's the last transport. Han, Leia and C3PO leave, but what about those she ordered to give the code signal? Han and Leia just leave them behind.

Leia tells them to get to their transports, but C-3PO says there's only one transport left, and it's their last chance.

At the point that Leia gives the order, a slim majority of their medium-transports have managed to break the blockade, leaving only one last medium transport (identified as "Transport C One Seven" in the novelisation) remaining in the hangar at the base. There are, however, also several smaller cargo ships, A-Wings, Y-Wings and numerous X-wings that have been moved behind the Southern Ridge of Echo base by their droid pilots These would appear to be the "transports" (plural) that she's referring to. These are going to be used by the the soldiers on the front lines and the pilots in the snow-speeders to make good their escape.

The walls quaked even more violently than before. Ice chunks continued to fall throughout the underground base as the three hurried toward the transport ships. They had nearly reached the hangar where Leia’s transport ship was waiting, ready for departure. But as they neared the corner they found the entrance to the hangar completely blocked by ice and snow.

_{^{Empire Strikes Back: Official Novelisation}}

The majority of the remaining base command personnel (that Leia told to evac) seem to have made it to the last transport and/or were killed in the evac tunnel. Some presumably were stuck and remained behind to fight the Empire's advance into the base since Luke could still hear "the sounds of battle" as he left.

We don't know where the other headquarters personnel went, but they are clearly not with Leia, Han, and C-3PO when their way is blocked by a cave-in. Maybe they went a different way to get to the transport, or maybe they had gotten ahead of the main characters before the cave-in.

In any case, it is not not Solo's responsibility to keep track of where they are. The captain and crew of the transport seem to be waiting on Leia's arrival, and so Han informs them that she is not going to be able to make it to their takeoff site. Presumably, they are waiting for the other headquarters staff who are assigned to that vessel as well. Han telling the transport to "take off" does not really mean that it is going to leave immediately, stranding people still left on the ground; it just means not to wait for Princes Leia.

Finally, we also know that the last transport is not the last vessel to leave; there are other, smaller craft still on the ground at that point. The Millennium Falcon is one of them, as are the small fighters. While there isn't enough room to catch a lift in an X-wing, there may be other intermediate-sized vessels capable of taking on additional passengers if they do miss the last large transport.