A report into a children's home run by Derbyshire County Council found that the home was unable to meet the needs of the single young person staying there.
Inspectors said that despite a decision to remove internet-enabled devices from the home to prevent him accessing pornographic websites, the supervision arrangements were not extended to the use of televisions.
"The young person has been accessing adult television channels," the report states.
"This omission means that young people with known sexually harmful behaviours have continued to access inappropriate sexualised material."
The report said that although the young person has very complex emotional and psychological needs, there was an absence of direct therapeutic work with him.
And despite risk assessments and psychological assessments for the young person stating that he is at "extreme risk of harm, or causing harm, when missing from care", he went missing on seven separate occasions.
"The whereabouts and activities of the young person during these periods are not always known," the report states.
"On one occasion, the young person claims to have been accessing the internet in a public place.
"On another occasion, staff observed the young person running in front of a moving car, leading the driver to make an emergency stop.
"Consequently, despite high levels of staff monitoring, the arrangements are not effective to safeguard this young person."
A spokesman for Derbyshire County Council said: "The safety and wellbeing of children in our care is a top priority and we take the concerns raised by the inspectors very seriously.
"We acted immediately to address the issues raised by the inspectors who acknowledge we have had a positive impact on this resident.
"We are always looking at how we can best meet the needs of children and young people in our care and our staff have undergone specialised training to help this resident.
Another children's home in Lancashire, run by Keys Childcare was also judged "inadequate".
Inspectors said young people were left at "serious risk of harm and criminal exploitation" when they went missing from care.
Ofsted found that the home was not "effectively managed," and stated staff "are not sufficiently qualified, skilled or competent to meet the needs of young people".
The inspection did find, however, that the residents benefited from the staff's "enthusiasm to find and promote age-appropriate community activity that reflects their diverse interests and skills".
A spokesman for the home said Ofsted's feedback "has been taken very seriously and a robust and comprehensive action plan is in place".
"The home is receiving senior management support and additional staff training is under way to reinforce knowledge about policies, procedures and best practice," they added.
"We are confident we have made significant progress on addressing the issues raised."
Meanwhile a West Yorkshire children's home, run by Timeout Homes, has been rated "outstanding".
Inspectors found that children had "highly personalised, well-integrated education, care and therapy".
"Children's safety and welfare is taken very seriously and their protection is central to how they are cared for," the report stated.
It also noted "exceptionally good relationships" between children and staff.
The home's manager, Chensena Dunn said: "The children have come a long way. It is really satisfying, and good that is has been noticed externally."