My GP says it is the safest pain med to use.
Like any drug, overdosing can cause problems.

Found this in Pharmweb, and is typical of other entries that I found.

Q:If paracetamol products are used long term, is there a risk of liver damage?
A :Many people use paracetamol for extended periods under supervision of their GP. There is no evidence to show that, at recommended dosages, paracetamol causes liver injury when used for long periods (4).

I have many intolerance's so my issue may be different than others. Meloxicam made me very ill..caused panic/anxiety attacks, severe pain just under my ribs, vomiting, and I even passed out. I stopped the med that day and this was only 4 days into using it. I was sick every 2 or 3 days for 2 to 3 weeks afterwards and am just beginning to get over it. My rheumy still wants me to try other meds and I refused. I had to go back on Celexa for the panic, I just can't seem to overcome them now. I, like Mrs. D do ok with Aleve and told him I will use it.

I was recently diagnosed with fibromyalgia and osteo arthritis.

Yes, and from what I've read, your dosage is pretty high. It's within limits for short-term daily use, but high (1330 mg) for single dose - 1000 mg. is the recommended maximum within a 6 hr. period. (Yes, I see it works out proportionally) For long-term use (longer than 2 weeks), the recommended maximum is now 2600 mg./day (which comes out to 2 - 325 mg tabs every 6 hrs.).

Something to look into is the supplement NAC (N-acetyl cystiene). It's what hospital ERs give patients for tylenol (acetaminophen/paracetamol) toxicity/overdose. Taken daily, it may reduce/avoid potential liver damage from paracetamol.
See: http://yarchive.net/med/tylenol.html

I've been taking acetaminophen/paracetamol with NAC for many years now. I just had my liver tested again this past week and it is well within normal.