Nothing wrong with the 737 pressurisation system as such. There is however a problem with the Boeing checklist policy for the after take off checklist which states that the PNF challenges and responds to his own actions. In other words the PF is not required to verbally answer the after take off checklist and in the simulator I have frequently observed the PF being so engrossed in the flying the aircraft either manually or by autopilot, that he rarely looks up to double check the actions of the PNF.
This frequently leads to an inadvertent mis-switching of the bleeds and/or pack switches going unnoticed by the PF who hears the PNF reading out the after take off checklist challenge AND response and assumes because the response is correct that the appropriate switches and pressurisation instruments must be correct.
Boeing states that the after take off checklist should be called after the flaps are retracted. This allows an early check of the pressurisation of the cabin IF that check is done correctly by the PNF. However, it is common for airlines to add more checks to the after take off checklist. These may include such minor items as seat belts and landing lights off at 10,000 ft. Thus the after take off scan and checklist is not accomplished until much later than Boeing recommend and a defect or mis-switching of the pressurisation system can go unnoticed until too late.
The Boeing after take off checklist does not specifically mention that the cabin pressure instruments should be included. It only mentions bleed and pack and isolation switch position. Of course a wise pilot knows that the cabin pressure and rate of climb is a vital key in the checking of the pressurisation. But there are pilots that stick rigidly to the words of a checklist and fail to think outside the square. In other words unless it is laid down in checklist form the pressurisation instruments must also be checked as well as switch position (in the after take off checklist and scans), some pilots simply don't check these instruments.
I can sympathise with Boeing who assume that people that fly their 737 are properly trained when in fact there are those who rely blindly on a checklist to tell them what to do. That said, I consider Boeing should review the after take off checklist philosophy and add a specific pressurisation instrument check. Boeing should also change the checklist to have the PF respond to the PNF challenge and not to have the PNF challenge and respond to his own actions. That would go a long way to minimising the risk of missing of vital information relating to pressurisation.
Finally, consideration should be given to making it SOP that the pressurisation progress is confirmed every 5000 ft in climb and descent. This would decrease blind reliance on checklists to initiate what are really airmanship items.