[Lanor Fow]

NW aren't always primarily responsible for the boards. North is responsible for moving them to the next table after they have been played (law 8A2), but apart from that the only responsiblity mentioned (that I know of) that could be considered 'primarily responsible for the boards' would be:

"7D. Responsibility for Procedures
Any contestant remaining at a table throughout a session is primarily
responsible for maintaining proper conditions of play at the table."

This is usually NS, if there is such a pair, but neither pair could be remaining, or as in some rounds of a howel or an arrow swicthed round in a mitchel, it could be EW who are primarily responsiblity for the boards.

As to the question, both sides look at the bridge mate, and are therefore (imo) primarily responsible so I'd give A-/A-. I'd also argue that no matter who is responsible for the boards, the issue isn't what board was played, so responsiblity for the boards is irrelevant. I don't know of a law that says the boards have to be played in order. The issue was with the bridgemate, which both NS and EW have a role in.

[blackshoe]

First you have to identify the problem.

If you are supposed to enter information into the bridgemate about the board you just played and you do not enter the proper information, you are responsible for that. If you are supposed to check that information in the bridgemate is correct before you send it to the computer, and you do not do so, you are responsible for that. A- to both sides if an artificial score adjustment is required.

OTOH, if you are a moving pair, and you sit down at a table where there is a stationary pair, that pair, being responsible for "proper conditions of play" at the table, is responsible for verifying that the correct boards are in hand, and that the correct board to be played is on the table in the correct orientation. This is easy to do when the bridgemate tells them what boards they are to play in this new round - and also who their opponents are supposed to be. I think it's incumbent on the moving pair, though, to check that they're at the right table, and that the board(s) on the table are correct and in the right order. In this case I would suggest A- to the stationary pair, and A to the moving pair.