two ways that come to my mind are:
1. checking manually media before each backup or in a batch.
2. go for an SLA with the tape supplier that any backup going bad will call for a penalty on the vendor, or permissible limit is 1 per 1000 tapes and so on (any conditions that seem to be feasible, practical and realistic but useful for improving the situation), and once the SLA is in shape, you will see a drastic improvement in the supplies quality.
Additionally, certain libraries have media management functions integrated into them- I assume you’re using the 3494 library with 3590 tapes- you would be able to solve your problem with a (quite expensive) upgrade to the new TS3500 library. You might even be able to migrate your old tape drives in.
As it is, without changing hardware, your best bet would be to set BRMS up to use a idle drive to continually test media, and to ensure that you have a clean cleaning cartridge set to clean every drive periodically.