Ideally you should be able to stack one board on the other and see no light. I usually shoot for the ideal since it means less stress in the joint.
I suppose a little light might be ok but certainly not 1/16 of an inch. In relative terms I wouldn't consider that a little gap, I'd consider it a gaping hole.
As for gap filling abilities. Most common glues don't have any and what they do have provides no structural strength. Epoxy or the like may do the job but they won't take stain and, in a gap like that, will look like hell.
I'm not familiar with a busy bee but if it is a jointer and you can't get the joint so you can't see light either there is something wrong with the jointer set up, your procedure, or both. A properly jointed board has a flat face. Not partly flat, not almost flat, just plain flat. When you put two flat faces together there will be no light.
Accuracy in any joint tolerances can be summed up easily. The closer you get to perfect the easier the project will go together and the better it will look. The further off from true the joints are the harder it will be to stick things together and the sloppier it will look. After that it is up to what the individual woodworker's threshold for a good looking project is.