What’s the most important thing to look at, that no one ever looks at?

Look under the hood: plumbing, circulation, hydraulics.  They’re underground.  They’re not sexy.  No one talks about them.  And if they are second-rate, you can’t fix it, because it’s underground.  A well-designed pool will move all of the water in the pool uniformly through the filter, heater, and chemical system.  A poor system will keep circulating the top 15 inches of water, and hardly ever circulate the bottom 24 inches.

It’s not enough to have a main drain.  A pool with two skimmers and a main drain is probably taking 90% of its water from the skimmers and 10% from the bottom, because there is a huge amount of resistance caused by trying to suck water up nine feet vertically.  Pumps do not suck water up very well.  That’s why well pumps are at the bottom of your well and not in your cellar.

Hydraulics is too complicated a subject to teach you here, and your builder may not even understand it – there is no licensing requirement to be proficient in hydraulics in New Hampshire (Live Free or Die).  Ask what thought that builder has put into it – and it will have nothing to do with a bigger filter.  The most water a 100 gallon per minute pump can put through a 40 gallon per minute pipe is 40 gallons per minute.  After that, you are just wasting electricity and over-heating the pump.  In fact, do not be impressed by a high-horsepower pump.  It’s an easy way to impress the consumer for $50 on a $20,000 job.  What you need is a pump, filter, hydraulic design, heater, etc. that are balanced.

If the builder uses a wider pipe coming from the bottom than coming from the top, it shows that they made an effort to balance the hydraulics.  Or perhaps he or she used valves, corners, or multiple pipes to spread out resistance.  I wouldn’t worry about checking the accuracy of their calculations.  Just see if they actually thought about the subject, and if their explanation even seems to make sense.