Broken faces

I’ve been making a model based off of a cylinder recently. I was making some modifications around the top rim, and then I wanted to add a loop cut around the cylinder, but it only appeared on some faces, and when I went into faces mode, the dots at the center of the faces were all (for the most part) at different levels. Could anyone help me with this please?

Why have you failed to supply a link to your .blend file like you should do for ALL support questions.

If your mesh is not looking correct go and physically look at it to see what is not as you would expect.

Sorry about that. Do you know where I could host the file. As you can probably see, I’m quite new to this site. Sorry for the inconvenience.

Thanks a lot!
Here’s the end goal:

I am however trying to give it a low poly, cartoonish look, sort of like the style you can see in team fortress 2, but a bit more realistic.

As for the .blend file, I cant seem to find the button for that (even in go advanced), so I’ll post these screenshots for now:

Those faces that seems to have offset center points are not clean quads. They must be a Ngons. Look at there vertex around those faces. Try removing doubles.