I can't see a problem with measuring and definitely point out major snags, but you'll find it better to go through room by room, wall by wall, surface by surface with a fine tooth comb when the site manager isn't around for proper snagging.
I found the home demo (our most recent was Bloor Homes) useful because it was the only time we had the builder's undivided attention without the salespeople present, and he was probably just a little more honest and helpful as a result.
Get the location of all the stopcocks, shut offs etc. Fusebox. Meters. What is under each manhole cover? Where do the drains run externally?Any limits to the plumbing (we're on a pumping station below the mains sewer, so had the Three P's Only rule drummed into us.)
Make sure there is a destruction manual and warranty documentation for every appliance, and whether you need to register them yourself for warranty purposes. Keys for every lock (including windows, garage, etc). Allen keys for toilet seats.
Which internal walls are partition walls only, and which are solid/insulated? Which external walls are not insulated (integral garages often aren't)?
Which wires and pipes come from the ceiling down, and which come from the floor up? Is everything buried in a wall aligned vertically? Where is the TV aerial cable in the loft?
Find out what make and model the bricks, tiles, grouting, flags, and paint are, in case you need to match them in future.
Ask them to show you how to re-pressurise the boiler.
And, depending on what you think of them as well as the quality, are any of the tradesmen (electricians, plumbers etc) still on site interested in - and permitted to - moonlighting for you, for adding extra sockets or taps, changing light fittings, etc once you've moved in. Often cheaper than getting your own in, and of course they know their way around.