I carried out an intermediate air pressure test last week on a house aiming to have a much lower air permeability than Building Regs requires and has heaps of insulation in the walls. A local window supplier had put in very high spec triple glazed windows, but unfortunately there were some issues with the way they had installed them. There was air leakage around the fixing brackets and in places joints in the internal skirts had been sealed with duct tape (the builder himself had diligently taped all other junctions in the building with air tightness tapes). This problem would not have been evident without doing an intermediate air pressure test on the building and the air ingress would be there for the lifetime of those windows.
An intermediate air tightness test is carried out while everything is still accessible, making faults easy and cheap to rectify. I use a thermal imaging camera (plus smoke sometimes) to detect faults. If the builder has not had experience of low air permeability buildings, I would always suggest an intermediate test is carried out as it lowers the risk of the building failing the on-completion air tightness test and reduces the level of stress for both client and builder during the project.
For timber frame, the ideal stage for an additional tests to take place is when the airtightness membrane is installed and still exposed (or after first fix where membranes are not used).
For masonry construction, a test is often carried out when all the airtightness tapes are in place, but the building has not yet been plastered. A test at this time will not give a quantified result, but will confirm that no taping has been missed and it has properly adhered to surfaces. A further test is then carried out after first fix.