Hi mushroomgod - the "tangent" mode for sweep is for a special setup where you have all cross-sections being planar slices all arranged to be on parallel planes, some details on that here:
http://moi3d.com/1.0/docs/moi_command_reference7.htm#sweep
It doesn't look like your profile curves are all on parallel planes, so that option won't do anything for your case.

Right now MoI only has some limited tools to ensure smoothness - you generally need to use the Fillet or Blend tool for that, commands such as Sweep or Network do not right now have the functions inside of them to adapt the surface to maintain smoothness to an already existing one.

So generally the method is that you don't actually try to make them smooth yourself directly when your surfaces are first created - make them intentionally creased and then put a fillet in between them to make a smooth connection automatically. If you check out those steps I was using previously in this thread here:
http://moi3d.com/forum/index.php?webtag=MOI&msg=2164.2 that i the method that I was using there.

In the example that you show, you're basically trying to do the fillet's job all built into the sweep at one time - that is not going to work in MoI currently.

In the future I do want to add some more options into sweep and network to ensure smoothness with adjacent surfaces, but those are some fairly advanced surfacing techniques, it will be a while before those are added into MoI.

- Michael