We also don't collect references any longer. Found it to be more trouble collecting than it provided any true information. We use the interview and background check as our primary screening method, like Jamine.
Also that gut feeling, if something doesn't feel right in the process, it probably isn't. For example, someone who calls with way too many questions when the information is available from other sources, or seems to eager to get started, or you find yourself working too hard to get information from the applicant because the person answers the questions with one word answers.
Stop and think, how many individuals do you actually turn down based upon a reference! I bet you will realize you are spinning your wheels.