Could you explain said border case? (I haven't bothered looking at the link)

What you're asking for should be pretty straightforward. I can only really invision three collision cases:

• sphere with side
  
• sphere with edge
  
• sphere with corner

The first is very similar to testing for AABB collisions, and the last is almost identical to sphere-sphere. The second is a little trickier I guess, I'd be projecting to a plane to which the edge is normal (for AABBs that's effectively just ignoring a co-ordinate) to effectively turn it into a 2D circle-point problem.

If you provide a little more detail on motion (obviously the nature of motion of objects involved is typically very important in a priori), I might be able to give a better response.

I'd be a little surprised if the code you found there was incomplete. What's the border case you refer to?

Well, that sounds like an ill-conditioned numerical solution. This stuff is always a bit of a bitch.

I imagine you should have sphere-edge down to circle-point, no? Looking back on some working I did on this stuff a while ago, circle-point (or hypersphere-hypersphere in general) is a quartic problem under constant acceleration, or a quadratic problem under no acceleration. I know of situations in which quadratic closed forms can go ill numerically, and I know of work-arounds to that; but quartics and other means are another kettle of fish entirely.

Could you be more specific about which (regardless of whether or not it's either of these) your situation is? I cbf looking at jyk's code, especially given it may or may not be relevant to your problem.