Digestive problems are so common with long-term use that some doctors think that they should co-prescribed with omeprazole and other agents to head them off. (Long-term omepraloze will give you B-12 deficiency if you don't supplement; it is an unusual side effect, but I can't sleep if I take omeprazole.
Cardiovascular risk from Vioxx was enough to pull the drug from the market; risk is also seen with Celebrex and other COX-2 selective NSAIDS. The risk with non-selective NSAIDS is less understood but still present.
My doc does not want me taking acetaminophen because she thinks it causes me to get elevated liver enzymes.
Like opioids there are problems when people don't "use as directed". My grandmother used to take Bufferin by the handful and one day at the dinner table we saw her throwing up blood like something out of a horror movie and she was subsequently hospitalized..
Acetaminophen overdoses can easily destroy your liver and are one of the most common forms of fatal poisonings.
The verdict is that we don't have truly 'safe and effective' medicines for pain in 2017.