The phrase "oversee every aspect" is correct and usable in written English.
You can use it in a sentence when you want to say that someone is keeping an eye on all the details of a situation or process. For example: "The manager assigned two supervisors to oversee every aspect of the project."
He famously promised to oversee every aspect of his team, from "socks to jocks".
The proposed organization, the United States Office for Contingency Operations, would oversee every aspect of rebuilding, including contracting and budgeting, according to the plan outlined in the report.
He has had to raise money for prints and advertising — a worthwhile trade-off, he said, to retain ownership and oversee every aspect of the release.
And they threw a spotlight on the influential five-member election commission, which has been given broad powers to oversee every aspect of what is supposed to be the country's first fair presidential election, with virtually no oversight.
The rescue was essentially an informal, high-speed bankruptcy reorganization that turned Long-Term Capital's creditors into its new owners, who will oversee every aspect of the restructured firm's existence.
Even when CEOs understand that they cannot oversee every aspect of their companies, they nevertheless assume wrongly that they will be able to learn everything they need to know.
Perry still oversees every aspect of the production.
It oversees every aspect of the rocket's design and operation.
From the beginning, Mr. Hefner oversaw every aspect of his creation with what one admirer describes as "a laser eye".
"It was a very intense renovation," Ms. Webster said, particularly since they oversaw every aspect of the project themselves.
Smith oversees every aspect of his artists' careers, from their wardrobes to their personal development as Christians.
