Presumably, if a teacher’s on the reference list there might still be a kesher, or a personal kesher to the family. Ask the teacher if her information is old or current. Ask the teacher for names of friends.
And find some IRL people – older friends who’ve been through this, a friendly rebbetzin – for concrete hadracha on how to do background checks.
And when you need a good laugh, track down the CSI:Shidduchim video.