Thanks for your reply. I don't rip DVDs with Handbrake. Most of my problems are with DVDs purchased in the late 1990s. Back then, the studios sometimes did a poor job of going from film to digital. Some of the DVDs are in letterbox format. Some progressively go out of sync because they didn't correct for the dropped frames. Others are out-of-sync from the start. In those cases, I feel like I'm watching a badly dubbed foreign movie.
My DVD player doesn't have skip frames or hardware acceleration. It's an older JVC that I like because it's multi-region. (I have some British and German DVDs.) If there's a DVD player that isn't too expensive that has adjustable audio sync correction, I'd be interested. I've searched but cannot find one.
I'd hate to do it, but the only solution might be to buy later DVD versions of the out-of-sync movies, although some (like Road Warrior) use the same crappy version in the newer releases.