How do I get bevelled edges from the inside of a mouth?

EDIT: Unsure how I solved it. Someone commented the corrected file, but idk how they did it.

I'm currently creating a face rig, and I'm at the modeling point of the process. I have all of the modeling finished except for one part that I want, but do not know how to do. Here's what the face looks like (for reference):

As you can see, everything is looking quite smooth. What I want to do is have the corners of the mouth beveled so that it isn't a rectangle mouth, but a roundish rectangle. What I want is red, what I have is black:

In edit mode I discovered that the edges of the mouth are glitched out. When I try to subdivide the faces, it isn't divided into fourths, but vertices are added at the edges instead, which is not what I want.

I know that I need bevels or subdivisions to do this, but the faces are just too glitchy. Can someone give me an alternative approach? If you can teach me how to do it with mean crease, here's a picture of what edit mode looks like:

Mouth edge, same on other side

Thanks for reading, I hope you can help! :]

EDIT: Here's what I was looking for. It's solved:

[UPDATE] Here's the file: http://www.pasteall.org/blend/36339

• I think you may start with this - i.imgur.com/TEi18ZP.jpg. (blend file is this - pasteall.org/blend/36343). I also think there are a lot of problems with that model, particularly with topology. You couldn't achieve roundish edges on the original file imo. You might want search for "good topology" in google (like this lesson - cgcookie.com/blender/lessons/topology-overview-human-head), because I changed only mouth, while everything else was left unchanged, but it should be. Good luck! Jun 1, 2015 at 13:24
– user1853
Jun 1, 2015 at 16:37
• @MrZak can you please write an answer detailing the steps that you took to correct the file? The idea is that others facing a similar problem can learn and not have to rely on you fix it for them.
– user1853
Jun 1, 2015 at 16:40
• @cegaton Whether it is really correct fix to make it as public solution? Also, I didn't understand whose fix used OP when saying that the problem is solved and who was that "someone" who "commented the corrected file". Jun 1, 2015 at 16:53
• Looks cool @MrSquer. Do us a favour and in true Stack Exchange style write a small answer to your own question, so you can accept it. Else no-one will ever know what happened here if they find themselves in a similar sitation they mind want to try the same. This is the "Exchange" part of what we do here. Jun 1, 2015 at 17:35

The original file is this:

First, I removed 129 doubling vertices (W -> Remove Doubles).

After some basic tweaking (dissolving some edges and adding 2 loopcuts to make vertices adjacent) got this

Now, mouth and teeth form. I decided to drop original vertices of teeth and combine them with loops of mouth and of the hole head. To do that, I deleted top teeth vertices (X -> Faces), selected one vertice from base of the top teeth and one from base of the bottom teeth and pressed J to make edge.

I did that for all adjacent vertices forming base of teeth. Then, I added loopcut (Ctrl + R) across the all head. I combined it with the top mouth edge so it to let me add more loopcuts without creating NGons:

Then I added 2 loopcuts across the head including mouth. I scaled them to 0 by Z axis (S -> Z -> 0) and moved slightly by Z to make teeth slightly smaller. Then I began recreating teeth by simply selecting adjacent vertices and pressing F:

After bottom teeth were done, I added adjacent quantity of vertical loopcuts (in this case 6) across the mouth to let it have roundish edges. Finally, I added Subsurf modifirer and set subdivision level to 2.

There are a lot of problems left, the eyes and whole top part of face should be rebuilt also or the eyes would not be seen as they should be. Also, my approach creates a lot of additional geometry - I tend to not creating NGons so Subsurf working as good as possible.

This is what I did. At the same time, I'm not sure what did OP to make his final image.