I assume you mean stuttering during playback. Have you tried playing back the files in question in different audio players, just to see if it happens in all players? I'm wondering if the error is in the file or in the playback program.
Also if you use dbPoweramp to rip (I think JRiver has the same feature) your rip checksum is validated against a database of everyone else's rips, so no possibility of an undetected error. Depending on what program you're using to rip, "Secure" might just mean an assurance from your CD drive that it thinks the data is correct, nothing more.
When I have had a small number of discs that were problematic to rip, I was able to rip them successfully in a different drive. Do you have the option to try a different drive, especially a different brand? I have two PCs in my house, and I always make sure their optical drives are from different manufacturers for just that reason - a second opinion.