Southport and Ormskirk Hospitals NHS Trust was inspected by the Care Quality Commission (CQC) in April.
Although overall care at the trust was "good", Southport and Formby Hospital did not give sufficient priority to safety in urgent care, said inspectors.
The trust said more nurses have been hired while A&E standards had improved.
Inspectors visited Southport and Formby District General Hospital, Ormskirk District General Hospital and the North West Regional Spinal Injuries Centre.
They found "significant improvements" at the spinal unit and in maternity services -  both previously rated as "inadequate".
But inspectors found the A&E department and surgical services at Southport to be "inadequate" with patients waiting "too long to be seen and assessed".
Concerns were also raised about a shortage of doctors, consultants and nurses.
Overall, the trust's services were rated as "good for being caring" but the trust still "requires improvement" in being safe, effective, responsive and well led, their report said.
Chief Inspector of Hospitals, Professor Sir Mike Richards, said delays affecting patients at A&E, as well as risks to safety in surgery, "must be addressed".
In a statement, the trust said it recognised that "a great deal more needs to be done" and A&E in particular needs to "rapidly improve".
A spokesman said the trust plans "tackle these issues" along with other ongoing quality concerns.
The inspectors' findings have been made public following disciplinary action taken against two senior members of staff at the trust.
Former chief executive Jonathan Parry was sacked for gross misconduct last month after an investigation into complaints from whistleblowers.
And former human resources director Sharon Partington would have been dismissed for gross misconduct had she not resigned, said a disciplinary panel.
The nature of the allegations has not been revealed, but the trust said no aspect related to patient care or safety.
A hospital's A&E department where patients had to wait up to 11 hours in ambulances has been rated "inadequate" by inspectors.