It really depends on what geometry you have, usually singularities will cause issues for: shelling, thickening, fillets and offsets. I believe the biggest trouble will be with shelling or thickening, as the program will attempt to make offset surfaces and fail.
So if you're not having any problems, leave it.
If you're having problems, try and remove the surfaces with singularities, you can check with Face Curves if you see a little red dot and the U-V lines converge to a vertex. Then use Delete Face and put new a surface in with Boundary- or Fill Surface.
Yeah, what he said. If it causes a problem then it's a problem. You can look at it closely with face curves or reflective surface or curvature display to see if there are ripples or a black area near the singularity. Those are all signs of trouble. You can also trim out an area and remodel it. It doesn't matter if the singularity exists at some point in time, it just matters if you try to do something to it when it exists, like shell or thicken. You often can't avoid making the singularity (or degeneracy), but you usually can avoid using it by cutting out and remodeling just that area.
I don't know of any way to predict (before you make them) which ones will be ok, and which aren't, it's "experimental science".
Thanks! It makes a lot more sense to me now when you explain what to do with them when they happen instead of just trying to avoid them.