Have a look at the current 737 after take off check list. It mentions four items.
Bleeds on, Packs auto, gear and flaps. now look at the amplified procedure in the Vol One. It says "After flap retraction is complete: Set or verify that the engine bleeds and air conditioning packs are operating, Set the autobrake selector to off, set the landing gear lever to off after landing gear retraction is complete - then do the after take off checklist.
This procedure and subsequent checklist is challenged and responded to by the same pilot - the PNF. The concept of challenge by one pilot and cross-checked and then responded to by the other pilot is negated. Not much point in having the same pilot answering to himself, is there?
The glaring omission in the 737 after take off checklist is there is no FCOM specific check of the cabin pressurising by observing the cabin diff or cabin rate of climb. The original 737 checklist from years ago - until it was fiddled with by Boeing - included the specific checklist item "Air conditioning and Pressurisation System....Check" That meant ensuring the bleeds and packs were in the required setting AND the two pressurisation instruments indicating pressurisation is taking place.
What we often see as trainers, is the PNF only observing the items stated in the after take off checklist - the four items mentioned earlier. Rarely does the PF look across at the switching while the PNF does his own thing of challenging and responding to himself. The essential aim of the challenge and response is shot to pieces when the other pilot is too pre-occupied in monitoring the automatics to concern himself with what is occurring across the other side of the flight deck -and in any case he is not required to respond anyway so it takes him further out of the loop.
If for some reason the aircraft is unpressurised right from the start of the flight, then with the pressurisation in the auto mode, excessive cabin rate of climb will trigger a master caution as the pressurisation system automatically mode switches to standby. You can't miss that happening. But if the take off is planned that the Standby mode is used for the flight, this alert is negated.
To test (train) if the crew are awake to the fact the aircraft has failed to pressurise after take off, it is possible for the simulator instructor to insert a fault that prevents the aircraft from pressurising. The alarming thing is from our experience, even with trained crews, that the majority of crews fail to notice the pressurisation instruments are indicating the aircraft is not pressurising. And why is this? - because the checklist does not specifically state to look at those vital instruments and the failure of crews to use commonsense airmanship instead of relying blindly on a written checklist.
Boeing may argue that if the packs and bleeds are in the correct position the aircraft must be pressurising. Not necessarily so, as witness the ill-fated Helios airlines 737 flight where the outflow valve was open for the entire flight. The solution is to re-instate in the after take off checklist the first item as "Air Conditioning and Pressurisation....Check - and then change the checklist policy to have the PNF challenge and the PF to respond rather than a one man band job by the PNF.