The Care Quality Commission (CQC) said that staffing pressures at all three sites run by the Mid Yorkshire NHS Hospitals Trust meant that some of its services were "not of an acceptable standard", but there was praise for the progress that had been made in other areas.
The health watchdog reported that a backlog of patients needing follow-up appointments should be addressed and that safety on Pontefract Hospital's stroke unit was inadequate.
But CQC inspectors also said that feedback from patients and relatives was positive, staff were kind and compassionate and employees enjoyed a more "supportive culture" than had previously been the case.
They said that a number of improvements had been made since last year.
In its report following a month-long inspection of the trust during the summer, the CQC said: "The trust did not always have the appropriate numbers of nursing staff and junior doctors to ensure patients received safe care and treatment within some services.
"We found that nurse staffing was impacting the ability of staff to provide compassionate care on the Pontefract Medical Stroke Rehabilitation Unit. For example, we observed call bells ringing for more than five minutes and patients calling out for help.
"The ward was consistently short of nursing staff.
But in praise of the trust, inspectors highlighted some areas of what they deemed to be "outstanding practice".
These included the formation of a School of Nursing in Dewsbury, which is currently the only one in West Yorkshire, and which it is hoped will alleviate pressures on frontline staff.
The way the trust took concerns of sick people and their relatives on board was also noted.
The report said: "The critical care unit at Pinderfields hospital had shown a dedication to listening to and involving patients and families.
"We found significant improvements in the culture of the organisation. Staff reported an open and supportive culture where concerns could be escalated."
The trust was given an overall rating of 'requires improvement', and its progress will be monitored by the regulator.
In response to the findings, trust chief executive Martin Barkley said: "We are absolutely dedicated to improving our services and this report clearly reflects that we have made progress in the last year, providing further independent evidence that we are an improving trust.
"We recognise, however, there is more to do. The CQC rightly highlights ongoing challenges around numbers of nursing and medical staff and, despite national shortages, we continue to step up recruitment of new staff as well as introducing initiatives to help retain the staff we have.
"Despite the challenges of limited resources and ever increasing demand on services, it is a testament to the hardworking staff on our wards, in theatres, clinics, laboratories, workshops and offices that we continue to improve as we move further towards our ambition of achieving an excellent patient experience each and every time."
The Local Democracy Reporting Service