I can't post links, but on a physicists blog (Google "black hole without singularity", it's first hit), he speculates it's possible to achieve a black hole without a singularity.
He's right. His particular proposal may not be valid, but it's certainly possible. In fact, I just posted along these lines in another thread. The thing with singularities is that they're a mathematical phenomena that don't necessarily correspond to physical reality. Most of the time when we come across one, it actually means that the theory your using breaks down and can't handle what you're asking it, not that there must be a real physical phenomenon there.
The popular view of a black hole is that you have a point with zero size but finite mass, and therefore infinite density. But we already know that general relativity doesn't give the right answers when you get down to very small scales, which is why one of the big challenges in modern physics is to get a single theory that agrees with both general relativity at large scales and quantum physics at small scales. So sure, GR gives the simplistic idea of a single point of infinite density, but it's in an area we already know we shouldn't expect GR to give us a reliable answer. So there may well not be a singularity, and most theoretical physicists will hope there isn't because dividing by zero is never a nice result to end up with, but we just don't have a theory that tells us what really is going on yet.
As for his particular solution, yeah, it's nonsense. All he's done is claim that you can take the mass of a neutron star and make it out of bottom quarks instead so it's smaller. That's not how physics works. You can't just replace a bunch of particles with different particles and expect everything to behave exactly the same. As ben m says, his
quark star (note that this is not an original idea) would have to be stronger than it is possible for anything to ever be. It's essentially the same as if he said "It's possible to get out of a black hole. Imagine something that travels faster than light. See, you can get out!". Sure, if you imagine something that, as far as we know, can't exist, then you can do all kinds of crazy things. That doesn't mean they have anything to do with the real world.
If it didn't have a singularity, could you get out?
No. Not being able to get out is pretty much the definition of a black hole. Whatever the details of what happens inside the event horizon, you can never cross back out.
Or do all your future paths (not phrasing that right, I'm sure), still terminate in the center of the black hole, even if it doesn't have a singularity?
Even with a singularity you don't necessarily end up in the centre. Not all singularities are simply a point, they can be torus shaped, and probably various other more interesting shapes as well. GR says you'll definitely end up at the singularity though, it just won't necessarily be a single point at the dead centre.