Paracetamol is probably as safe as it gets when it comes to drugs in its class. Overdosing is not all that simple and the numbers are high because of the availability and popularity of Paracetamol as a pain-killer and its silent use as a side ingredient in many products. Paracetamol is not as good as Ibuprofen when it comes to killing pain (IMHO), so maybe this causes a tendency to overdose in people who have built a tolerance to the drug.
To get liver damage, you have to exceed the daily recommended maximum of 4g of Paracetamol. Wiki says paracetomol toxicity is likely if your consumption exceeds 7g in a day [1]. Assuming you are a consuming Paracetamol in the form of OTC pills, say the super strength ones which are 500mg, you have to consume like 15 pills in a day. Overdosing from a combination of drugs containing paracetamol is much more likely. Most people don't realize the presence of the other ingredient.
For short term use, Ibuprofen is said to have a similar safety profile to Paracetamol, though its classification as an NSAID lends to its perception as a slightly less safe drug. Long term, it causes stomach and kidney damage.[2]
Anecdotally, Ibuprofen is much better at killing my pain, but I also have some negative reactions like increased reflux. Technically, Paracetamol also increases acidity but I tolerate it much better. I've mostly stopped using NSAIDs but I realize this is not possible for a lot of people.
[1]: https://en.wikipedia.org/wiki/Paracetamol_poisoning#Cause
