We had to deal with that issue at our club. To clarify we decided to include the following wording in the Eligibility and Entry section of the NOR. 
4.4. An eligible boat shall check in by sailing, with its mainsail hoisted, past the transom of the Race Committee signal
vessel. The Race Committee will acknowledge the check in with a hand signal (thumbs up, ok, or wave). A boat need
only comply with this process before her first race of the day.
4.7. Once checked in, a boat is considered having come to the racing area for all the races of the day.

I have felt is necessary for the NOR or Si's to read sail by the stern of the Committee boat on STARBOARD otherwise with small boats or a large Committee boat you have collisions off the stern when checking in. Starboard you get a clear read of the sail nimer and a parade of boats.

Since A5.3 does not specify when a race in a series starts, and since there is a separate section for series scores (A2), I think it would be interpreted as applying to each race. We find it is mostly to give credit to folks who at least try and race.
However, it is one of those rules that can be changed.  It is not excluded by rule 86. So if you find it is better to tweak it, just spell it out in the NOR or SIs. I would add that I can see a case for applying it for the day, for example if a boat retires in the first race due to equipment problems and are now unable to race again that day, at least they tried! But of course there is the other case where they did not intend to race the other races in the day.

I read as each race of the day. 
A boat that do not come to the starting area on the following race of the day, will be scored DNC for that race (one point more than the boat entering the series); and the boats  that came to the starting area, one point less for their DSQ, OCS etc
Tedious, and big headhache for the RC.
Reason to use the A5.3 is beyond my understanding.
 

Thanks Aldo, 

A5.3 is great to use for a long series such as a summer or winter series.  Every boat that registers may not come to every race in the series.  So if 50 boats register, and only 45 come to the starting area, without A5.3 DNS, NSC, DNF RET and DSQ would be scored 51.  I believe scoring for the number of boats that come to the starting area plus 1, 46, is fairer to the competitors. 

Some long series have a participation percentage knowing that every boat will not be able to compete in every race.  For example, to qualify for the series a boat must race in 90% of the races.  If they race in more, only the top 90% of their scores will be counted.  This is incentive for boats who reach the qualification to keep racing.

The rub is, as you say, it places an onus on the race committee to know how many boats come to the starting area.  For the first race of the day with mandatory check-in (SIs), that is easy.  But, if RC is required to determine how many boats come to the starting area for each race, it is more of a challenge.

IMO, A5.3 does a great job in solving the “large entry list vs weekly participation over a season” problem.    The chances that there will be a large difference between the # of boats that check-in the first race vs the last in any given weekly occurrence is pretty small .. equipment failure, serious damage, and thunderstorms on the horizon are the usual culprits. 

In these season events, some may enter knowing that they may only make a small %, and A5.3 does the job to keep those boats from really scewing the “penalty” for not showing up one day. 

That said, I rarely see it applied without modification, the most common being a finishers+1 for those who checked-in and finishers+2 for those who skipped the race entirely. 

PS: This also prevents sailing being a “game of chicken” (a test of nerves), if the weather seems marginal for that week’s race, as the penalty for not going out isn’t as high.  I think of it as having a safety benefit. 

I also read this as each race of the day since it refers to scores for start, sail the course, finish, DSQ or RET which would be per race.
Yes, RC must count boats that appear in the starting area for each race unless NOR/SI says something different.
Probably best for RC to raise Come Within Hail flag at start of each race for each fleet for starting area check in.
We use this for Wednesday Night Racing. However, we only have 1 race per fleet per evening.

In the previous rules this was covered under Appendix A9 automatically if the events was a long series.

You will find the most scoring systems can deal with this without you having to do an inventory of the boats for each race.  Sailwave has on option to enable A3 and looks after it.   Without any user interaction it can calculate based on the letter scores and finishers the number of boats that came to the starting area.

On a side note: High point scoring systems like CHIPS are very good for long series.

Just an aside: a club, competitors and other race officials should be worried if the race committee  was not closely monitoring,  the fleets recording boats that leave the course (breakdown, tired, etc.).

We use A5.3 in our summer weeknight series for all the reasons stated above. We have a OD series where there are 2 short races in an evening and not all boats sail both races. RC keeps close track of who starts each race but it is also the responsibility of the competitors under SI Safety Regulations to let Race Committee know if a boat "no longer intends to participate in racing".

Our radio sailing fleet has "seasonal" series in which any one day's participation can range between 4 and 15.
We recently considered invoking A5.3 in our General NOR, but that still does not meet our needs.
We are now going with the default A5.2, but adding "Each day's racing will be scored separately."

My humble opinion is that A5.3 is a gallant attempt to use THE scoring system in the long series stuff that runs for seasons or otherwise longer term where daily participation varies greatly. Personally I'm a fan of high-point scoring systems for long series, such as Cox-Sprague or CHIPs. It's one thing to win a race with 5 boats racing, quite another to win one with 20 boats. At the end of the day, A5.3 doesn't quite get there. Square peg in a round hole....