Wards, nurses and ancillaries
Theme Hospital's diagnosis and treatment was unrealistically quick. In real life, patients are sometimes tested and diagnosed over the course of months, not hours, visiting hospital on appointment when doctors and resources are available.
More seriously ill patients, esp. those awaiting or recovering from surgery, must stay there on wards, another aspect of medical life Theme Hospital barely featured and which plays a big role in planning hospital lay-out IRL. Doctors do diagnosis, but patient care--esp. on wards--is the responsibility of nursing staff. They are the ones administering treatments from the pharmacy, monitoring patients' vitals day-to-day, and taking samples for lab testing. It would be nice to see this reflected in Project Hospital.
Additionally, though nursing staff once changed patients' bedding, supplied bedpans and served food on wards, this is now mainly the responsibility of ancillaries. They're in Project Hospital already as cleaners--vital as much to stop spread of hospital infections (MRSA) as for mere tidiness--but hospital laundries and kitchens should also be part of basic design. If hunger and bladder bars already exist for patients waiting in corridors, why can't this mechanic be extended to those on wards too?
Incidental to this is hospital visitors and visiting hours to wards. Though these hours would bring increased revenue (and realism) to Project Hospital through cafeteria and gift shop sales, they would also interfere with diagnostic access to patients and bring litter, increased risks of infection, and the need for more restrooms, bins, and receptionists. The cafeteria could be supplied from the hospital kitchen too (BTW, not wanting to turn this into Sim-Cafeteria/Giftshop - 'rabbithole' space with price/service sliders might well be enough to do the trick.)
A last, unrelated thought: outside walk-in clinics, appointment / referral system makes most patient treatment predictable; players should know how many patients to expect, who will be treating them and what tests will be done on them at the start of every day (missed appointmnents excepted). Where numbers are *not* predictable and treatment is more urgent is in A&E (Accident & Emergency) and here additional factors in the number of patients arriving and their survivability are availability of ambulances and paramedics staffing them, their turnaround time, and effectiveness of A&E triage. It would be particularly exciting to model - and, given its unpredictability, to play.