Well, ibuprofen can cause ulcers and bleeding in the stomach and intestines i believe.
The damage paracetamol can cause to your liver is a different sort of damage - so i suspect that you'd probably know about it relatively quickly if you suffered problems from ibuprofen.
Having said that, i've never had health issues from either, so i can't speak from experience.
I'm pretty sure that even in the case of serious overdose, people who OD on paracetamol are can be asymptomatic for a day or two; but it is crucial for them to be treated in hospital as soon as possible, and the drug flushed out of their system by large amounts of IV fluids (possibly in combination with ingestion of activated charcoal. i could be wrong about the treatment - that is just off the top of my head).
I've heard of people ODing on paracetamol, but failing to present themselves to an Emergency Department until the next day - then after a few days (even up to a week), having their liver shut down, and dying.
From all accounts it is a really awful way to go, and in the case of suicide attempts, people sometimes change their mind - or think they have survived and experience a sense of relief - only to get very sick and die a few days later.
For that reason, OTC pain meds are really not something to use without a great deal of caution; really, people should be advised to stick to recommended doses - but for people looking to use the codeine recreationally, a cold water extraction is a must.
As stated above, it is safe to mix (therapeutic) dosages of ibuprofen and paracetamol - just be sure to follow instructions, such as not taking ibuprofen on an empty stomach.