Correctable error after half time.
 

The technical foul at the end of the half got me thinking about a CE at the end of the second quarter. Say there is a foul against A1 which should be a one and one situation but no one realizes. The in bounds the ball and dribble out the clock.
Coming out of the half time intermission the crew is notified that it should have been a one and one situation. I am pretty sure this is a CE situation, but am not quite sure how to go after that. If I had to guess, even though it is the start of the third quarter, POI would be AP arrow at division line after the FT(s) with the lane clear.

Ok. Ready go!!!!

I agree.

Situation 2.10.1 B talks about an error being found after time has expired in the game, but before overtime begins. It says that the error can be corrected.

Although we're talking about halftime in this case, I would think the error can be corrected. The ball wasn't made live after the first dead ball following the error.

Like you said, I'd shoot the "one and one" with the lane clear, then use the AP arrow to determine who gets the ball to start the second half.

I had virtually the same situation 3 season ago. Foul near the end of the first half. Table told us it was the sixth team foul (I asked specifically, "How many fouls on white?"). Play continued after the throw-in for the final minute of the half with no baskets or play stoppages. At the end of the half the scorekeepers tell us they goofed. My partner and I huddled and remembered the first dead ball after the foul was the end of the half. We told the coaches (thankfully, they were both very understanding), shot the FTs, then came out with the AP arrow to start the 3rd quarter.

At which end would you shoot? :D

That was a point which we debated on here several years ago. The 2nd quarter is over and the 3rd quarter has yet to begin. There are meritorious arguments both ways without a clear answer.

If it's discovered/handled at the point described in the OP I'd do it at their 2nd half baskets just to limit confusion (mainly mine).

In which quarter will the points be recorded?

Third, since the second is over.

But the 3rd hasn't started. And the foul for which they are being shot was in the 2nd.

If the situation were at the of the 4th with the score tied and before the ball became live for OT, would they be in OT or the 4th?

I really think this is just one of those areas where you can do either, however. It's not going to make any difference.

2.10.1 B provides for this same CE (not awarded merited free throws) to be attempted as a part of the 4th period. (tie game, if successful, game over)

Therefore, the throws are part of the 2nd period. Shoot the throws at the appropriate basket.

It's actually rather complicated and while that Case Play helps (and I agree that under those circumstances the prior quarter is the appropriate one for the free throws), it isn't the answer for all cases. Let me provide an example.

5-6-2 Exception 3 states that a penalty may carry over to the next quarter in the case of a CE.
Scenario: A1 is fouled while dribbling at the expiration of time in the 3rd quarter. The officials do not notice that it is the 7th team foul. The 4th quarter begins with the AP throw-in to Team A and after six seconds A3 is called for traveling. At this time the scorer alerts the officials to the failure to award FTs to A1.
You can't go back to the 3rd quarter now after playing six seconds of the 4th quarter! So the 1-1 in this specific case would be part of the 4th quarter.

I agree with the "prior quarter, at the prior quarter's basket" answer -- until the subsequent period has started.

The difference there is that the next quarter has already started with the AP throwin.

I disagree that either play would be complicated. If we apply 2-10 along with some common sense, we correct the errors and put the ball back into play with ease.

When we over think something like this, it then becomes complicated.