NSAIDs can have particularly unpleasant side effects.
Within the gastrointestinal tract, NSAIDs increase the likelihood of developing stomach ulcers. This is due to NSAIDs inhibiting the secretion of acid from mucosal cells (which provides protection from the highly acidic stomach environment). By co-administering misoprostol with long-term NSAID use, the risk of ulcer development can be reduced. Prostaglandins help to maintain renal blood flow, so administering an NSAID can reduce renal blood flow. This can lead to chronic renal failure, especially in the elderly.
Paracetamol (which isn’t entirely known to be an NSAID) is hepatotoxic. Its route of action is not fully understood, but it may inhibit COX1 or COX3.