All of the red lines are considered open edges in pepakura. One thing that will help is to go in to sketchup and make sure that all the faces on the model are the same color. Notice how in sketchup some faces are white and some are purple. This is done by right clicking on each face and choosing "reverse face". Also, you can highlight all the faces that you want to change at the same time by holding down the "shift" key while clicking on the faces and then reversing the faces. That will work everytime. Or, if you would like to do multiple you can try highlighting the whole model, right click on it, then choose "Orient Faces". This doesnt always work though so you may have to still do the first way after that. If there are still lines that show up as red in pep, they could be a few different things. The first is just random geometry. Sometime sketchup will "hide" things from you (im not sure why). To fix this, just click on edit, go down to unhide, and select all. then go around and delete anything it brings up. The other is just a random open edge. What you will have to do is create lines from the ends of the open edges to another spot on the model.
Ex:
In the picture above, both of the blue highlighted lines were showing up as open in pep. All i did was create the lines going down to that point and it fixed the lines in pep. I really hope this helps! if it doesnt, i could probably take a look at the model for you and figure out why its doing it, fix it, send it back to you, and explain what i did to it. Best of luck with your models, they look great!!!
Alex