How long will a pork butt keep

IMO, you should toss it. There is a good reason that some religions consider pork as taboo - it spoils rapidly. I had a severe bout of food poisoning from old leftovers, and I do not want to go thru that again, EVER. I now pitch all leftovers into the trash after 4 days max in the fridge.
You can't always tell by smell or taste if it is spoiled, and the toxins given off by the bacteria that cause spoilage won't be neutralized by reheating it. Why risk it?
Just my 2 pence worth.

There really are a lot of questions to this post that would help answer your question. Things like: What was the internal temp of the meat when it was "finished" and how was it cured? Was it put into a sodium nitrate or nitrite brine or was it with a simple rub and not cured? How thick is the meat? These are all factors of if it is still good or not.

Bottom line I agree with Gil food poisoning sucks! I've had it too and wow.

If you are conserned with it then toss it.

I keep mine 3 weeks and longer in the fridge with no problems, ever. Just make sure you cover and cool the meat after smoking.

After a week or so in the fridge, I usually will bring the meat to temp before serving to kill any microbes. If it is pulled, this is easy to do in the microwave.