Hi BlackBird - usually it helps to make things that you want smooth out of one bigger surface piece, see here for some explanation:
http://moi3d.com/forum/index.php?webtag=MOI&msg=1398.18
http://moi3d.com/forum/index.php?webtag=MOI&msg=1398.19

In this case are you trying to do this whole thing just as one single Network? You'd probably want to do it more by building each of the cylinder-like pieces on their own and then building the connector pieces as an additional step instead of trying to do the entire piece all in one shot with only one single network.

Another strategy you can use is to put in blends to make smooth connections - to do that you would trim out a little bit of space between the 2 things that you want to have smooth like this - here I use the Trim command to cut your surfaces back a little bit to leave some space between them:






Then select these edges:



And use the Construct > Blend command to put in a smooth connecting surface:



- Michael