Do the reference checking yourself. Doing the reference checking yourself can be beneficial. You are hearing the information directly and are in a better position to probe for additional detail if necessary. It is the little bits of information you gather that are often most revealing. Ask the right kind of questions.
Reference checks require as much skill in questioning techniques as selection interviews.
It is easy to fall into the trap of asking closed-ended questions that don't elicit the full response you need, or backing off when former employers seem reluctant to provide additional information. Sometimes what is not said can be as telling as what is said. Document the information you receive. Document the source of every piece of information you obtain about an applicant. Develop standards and follow them.