Substitution question
 

A1 is charged with his/her 5th foul of the game. The reporting official has informed the Head Coach and the 20 seconds for replacing the disqualified player has begun. After the first 5 seconds, the "warning horn" properly sounds. Then...A7 comes to the table to check in the game, but he/she is not the substitute for A1. Even though the "first horn" has sounded, the official allows A7 into the game, while waiting for the required sub. Is the official correct in allowing A7 into the game?

Yes. There are no restrictions on other substitutes entering during the replacement period. It is not a time-out and the warning horn does not have the same meaning as it does for a time-out.

Is this hypothetical, or something that you saw happen? Are you saying that A7 came in and another player besides A1 went out? Is A1 still on the court or what?

From the 2003-04 POE:
H.If a substitute from the non-offending team or a substitute from the offending team for someone other than the disqualified player reports to the scorer during the wait for the required substitute, they may enter the game. (3-3-1d)

I.A warning horn shall now be sounded at 20 seconds if the required substitute has not reported to the scorer’s table. This is an indication to the head coach that a substitute should report immediately (2-12-5). This warning horn does not have the same substitution restrictions as a warning horn for a time-out (3-3-1a); other substitutes from either team may still report and enter the game until the ball is about to become live. (3-3-2)

*Note that back in 2003-04 a HC had 30 seconds to replace a DQ'd player or a player directed to leave the game and the warning horn was at 20 seconds. This has since been changed. The current times for 2008-09 are a 20-second replacement interval with a warning horn 5 seconds into it.

Are you asking if A7 can come into the game immediately or if A7 must wait until the replacement for A1 reports? I think that the correct mechanic is to have A7 wait, but either way A7 gets into the game suring this period and I wouldn't make a big deal of it even if it is the "correct" mechanic.

What Bob said.