Chief Inspector of Borders and Immigration, John Vine, found the UKBA had allowed a backlog of 153,000 notifications from sponsors of non-EU students to build up, including whether students were turning up for classes.
This could potentially have meant that thousands were wrongly allowed to remain in the country, he said.
The tip-offs were all reviewed by May this year, but Mr Vine said it must be an "ongoing priority" to make sure checks are carried out.
His team examined work at three UKBA offices in Sheffield, Beijing and Delhi.
However, Mr Vine said his findings were "generally positive" and he was "pleased" the agency had reviewed the notifications.