Hello, I'm avail. at the moment and can try to help you.
Paracetamol is acetaminophen. Dogs do not metabolize acetaminophen as well as humans so if used, it must be done carefully and at the correct dosage for the correct period of time. For this reason, many vets don't use. acetaminophen for dogs at all. There are so many much better and safer drugs available (mostly NSAIDS) that are approved for use in dogs.
For a large dog the size of yours, however, the toxic dose is way more than one 500 mg tablet. 1 kg = 2.2 #, so your dog weighs approx. 50 Kg. 100 mg/kg can cause liver issues, over 200 mg/kg can cause methemoglobinemia. However, there have been reported problems at lower doses too. Your dog should be okay at the dose he got, but to be safe, you may want to talk to your vet about using an dog-approved NSAID instead.
Also, there are a lot of joint nutraceuticals out there that are safe and may help your dog long-term, usually chondroitin and glucosamine combos:
Best wishes for your pet!
In a pinch, you can use buffered aspirin safely for most dog (unless of course, he has a bleeding disorder, hemophilia, Von Willebrands, renal insufficiency, etc). Giving it with food is best so it doesn't upset his stomach. The dose I use is 10mg/kg. First I would just try 1 buffered aspirin with food every 12 hrs as needed, but if not effective, you can use two per dose. I wouldn't use it long-term either. Also, aspirin can interact with other drugs, and shouldn't be used together with other NSAIDS, steroids, etc.
Also, don't use ibuprofen or any other OTC NSAID. They can cause toxicity in dogs.