Optimal method to test an external hard drive?
Apple's Disk Utility doesn't have false positives but it can miss some errors. 

Although it's not cheap Disk Warrior is magic for these sort of problems, in my experience it's fixed all non-physical-damage errors that I could throw at it. 

If you're not keen to spend money, and if you've got the hard disk space, copying the contents off, repartitioning your external drive and copying back on on might clear up your problems. Copying the whole disk's contents (starting with what is most valuable to you, in case it dies while you're copying) is probably a good idea anyway, in case your disk is on its death bed.