I have a G0586 but I can't think of anything model-specific that would produce the symptoms you describe.
The first thing I wanna ask is which bed you set the fence to 90 degrees on?
Always set your fence to 90 of the OUTFEED table - that's the one that matters because that's what the freshly jointed edge rides on. If your jointer is setup properly, that it won't matter, but just in case. Also, are your knives 100% parallel with the outfeed table also? ALL of them - it's easy to miss one of the 4 knives, I have :P
Second, if the stock can't rest on the jointer through out the entire travel of it's run without someone holding it there, you'll be spending time holding it and that can throw the cut off.
If you're getting a tapered piece, that's normal with jointers. They're not meant to make parallel surfaces and nothing guarantees they'll take a uniform amount of wood off from one end to the other unless that edge is already perfectly straight.
If you're getting a bevelled piece (the fresh edge is not square to the face that ran against the fece), then it is likely a technique situation if the jointer's properly setup. If the face you're resting against the fence is more than double the width of the fence itself, it can get pretty tough to hold that thing square. It takes extra care, maybe even a couple really strong feather boards on the infeed table, to make sure it stays square all along the path of travel.
It's also possible to get a taper if your technique is off so just to be sure, let's review that: Rest the stock on the infeed table and turn the jointer on. Press it against the fence about 10% in from its leading edge and put your rear hand about 60-75% from the leading end, also pushing against the fence. Push the first 15-20% of the board through and then bring your rear hand up past the cutter head, pressing downward against the infeed table and forward to keep feeding. Now you do this hand-over-hand dance between your front and rear hands, each doing its respective jobs - at this point it becomes Fence hand and Outfeed hand - one presses against the outfeed table, the other presses against the fence until the entire length of the board is completely fed through. The idea is that you want to ensure you're referencing botht he fence and the outfeed table for the entire pass. This is why having to also combat the weight of an oversized board makes it practically impossible to get a good cut.
Hope that helps