Hey lb1 -
If you have a logo with a bunch of different parts and you want a fine white line around ONLY THE OUTSIDE BORDER of the logo, this is probably the best way to do it:
1. Select all of your logo elements by making sure all your layers are unlocked and click "ctrl + a" or edit -> select all
2. Copy the logo (ctrl + c) and make a new layer UNDERNEATH your original logo. Paste your copy onto this new layer by pressing ctrl + b or "edit -> paste in back" with the new layer selected. this will paste the copy in the exact same position as the original logo but on a new layer behind your orginal logo. At this point I would hide all your other layers except this new one so you can see it.
3. The next thing I would do, with the entire logo copy still selected, is "type -> create outlines", and "object -> outline stroke" on all the elements so that everything is a fill: there are no strokes or type. Make sure everything is selected when you use these commands.
4. The next thing is to combine everything into one path. Do this by -- with everything selected -- click the "add to shape area" button on the pathfinder palette. Make sure nothing is grouped for this to work properly by clicking "strl + shift + g" a bunch of times with everything selected before using the "add to shape area".
Now your logo copy should look like one complex shape of all the same color.
5. From here, if there are any holes in the shape you don't want to be there (maybe the inside of an "o" or something has left a hole in your shape) you can get rid of them by going to "object -> compound path -> release" then redoing the "add to shape area" thing to make one solid shape again.
6. Now that you have this one solid shape, choose a fill and stroke color. The stroke should be the white outline you want, probably one or two points in thickness, although you may want to make it thicker. If everything is done right, you should see a stroke only around the outside of the shape
7. When you show the original logo by unhiding it in the layer's pallete, the original should be on top, and what you just did should be on the bottom, with just the stroke showing from behind.
I hope this makes sense, I know it is kind of long. Let me know if you have any questions. Peace.