Strongeagle
As a non-newbie (50 years experience) I would advise you to 1. be patient. 2. check the fit before going for the glue. 3. take your time (be patient again) 4. use your glue sparingly (just enough to get the job done). 5. use a fast acting liquid cement. My favorite is Tamiya "Extra Thin" with the green top.
That is where I was going with what type of glue he is using. I follow the above as well and I seldom have the issue noted. I would add that for larger pieces I apply glue in sections, not all at once. When using Tamiya and the applicator that comes with it, you can apply glue sparingly, and exactly where you want it.
If you are not familiar with this type of cement, it is important to note that you can apply the glue along the join from the outside of the piece. Capilary action draws the cement along the join, and any cement that gets on the outside of the piece dries fast enough to where very little damage is done.
Since my return to the hobby I find Tamiya Liquid Cement is my favorite change from the old days of using tube glue. Next to that is the advent of sanding sticks, both are a must have in my work flow.
Good luck!