How about after the first FT?

First, I hope the official charged the team, not the coach, with the T.

Second, yes if the free throw has not yet been taken, you're not too late to fix it. If, however, the free throw has been taken, what's done is done.

An interesting question would be if the team would still have a time out left since they paid a T for their 5th timeout.

BILLY - I think your case and the OP are good object lessons in a "slow whistle" I know this usually applies to action on the court but it applies in both of these cases as well. Or you could call it preventative officiating.
In both cases I would make sure that I went to the table and confered with the scorebookS. The scorekeeper from the offending team will most likely have a different opinion in regards to the player or the TO. If they can't agree then I go with the home book, but this would give the home book an opportunity to "revise" their assesment of the situation. It would go a long way to preventing either of these situations. Because if you find yourself in this situation, your bacon is probably cooked regardless of what you do. IT is the archetype for a No Win:
Probable questions asked by your assignor -
Why did you issue a "T" in the first place?
Why did you rescind a "T" if it is not of the CE?
Why did you NOT rescind the "T" when there was no error?

In my very first game ever 2 days ago..we had a scorebook issue as well. Assessed a Technical.

Question: after adding the player to book, is player eligible to play in game??

I would say they do. This situation isn't specifically addressed, so I'd be willing to fall back on 2-3 here.

Why wouldn't he be?

Academically ineligible?:p

Or to steal a quote from Iowa Hawkeye football coach Kirk Ferentz regarding star running back Adam Robinson, "Academic indigestion."

Because he was not listed at the start of the game? Is there a difference between being on the roster eligible to play and being in the scorebook?

No. Once he has been added to the book it is as if his name was included from the start of the game.

The only reason to add him is so he can play. If he doesn't play, there's no need to add him.

Scenario: A15 comes in as a sub but isn't in the book. At the end of the quarter, long after A15 has subbed out (with no points or fouls), the table notifies you of the problem. Coach can decide not to add A15 if he's not going to play him again.

I seem to remember some constipation...I mean consternation surrounding this scenario on this forum.

Thanks for the clarification...one of the tips that my R showed me was to take a headcount of players during pregame and verify with coach that number and compare to the book.

Yup, and do this before the 10 minute mark so you can hopefully get it fixed without having to assess a tech for it. I caught this a couple of weeks ago when I noticed the visiting team was missing a player. Turns out the coach forgot to add her to the roster.

True, let me change it.

A15 reports to the table and the table informs the officials before play begins. Coach then has the opportunity to withdraw A15 prior to participation (perhaps his team has the ball and he desires to add the player to the book when it won't cost him a possession.)