Audio (or headphones) make shuffling sound

Does sound like the headphone jack's on its way out, but you can try reset the PRAM/SMC to see if that makes a positive impact.

Do you still have AppleCare?

 

I'm sorry to hear that. As a workaround you can possibly try purchasing a USB>audio splitter so it doesn't exhibit the same issue. Hopefully others have some more suggestions. What model/year is your Mac please? Due to its age we can run a few other diagnostics while we're here to identify any other problems.

 

This might sound odd, but have you had any issues with the monitor going colourful/freezing, synonymous with the below images?









The reason being that if you've had issues with that (colloquially known as Radeongate), you can get that fixed free-of-charge through your consumer law, as your model suffers from that -- and the repair would involve replacing your Logic Board, which in turn would fix the audio jack!