The backlog of 153,000 notifications could potentially have meant that thousands were wrongly allowed to remain in the country, the Chief Inspector of Borders and Immigration 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.
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Accompanied by the Duke of Edinburgh, the Queen will attend the opening ceremony of the fifth session in the Holyrood chamber.
Ms Leadsom has received the backing of Ian Duncan Smith, the former work and pensions secretary.
The former shadow work and pensions secretary is considered a more viable candidate than Angela Eagle, a Labour source has told ITV News.