When i first started building puppets 2 years ago, i learned from the foam book. So i wasn't aware of any other glueing method than the glue gun. By the time I even heard about contact cement I had already gotten hooked on the glue gun. It may seem like a newbie thing to some, but for me it does what i need.
As for sketches....Up until 2 years ago, cartooning and animation were my only real forms of character design. When I started building puppets, it was a lot of fun getting to create a character in a completely different way. You can't just draw it and see it come to life, you've got to cut those pieces out and glue 'em all together before you even begin to see anything even resembling a character. The transition was really exciting, but i've found that i'm totally unable to draw a design for a three-dimensional character. It just doesn't work for me. So i just use the building process as the sketching- in other words, I don't have a definate idea of what the character looks like before i start building, i just know who the character is. Only a few times has it come out completely terrible, but i think those times were when I had no clear character in mind when i started.
As for the mouth, how exactly did it get like that?
If you sewed the mouth inside directly to the head covering, you may need to make sure that the mouthplate sxtend a bit past the mouth coloring, to avoid the inside curling up like that, and to maintain a straight curve in front. Or you may want to consider gluing the head covering to the mouth so that you have direct control over the overlap there.
Hope that wasn't too lmuch.
Great puppet for a first try. My first looked like a rotting puppet corpse. It had flat felt eyes, creepy yarn hair, and hand sewn stitches that were like a cm apart in some places. And it was 5 feet tall.