Well I fixed the problems I was having with the camera. First, let me explain why I was having trouble. I had my planet centered at the origin (0,0,0) and I gave it a radius of about 6.5 million meters. I initialized the camera position to be right at ground level of the planet (6.5 million meters plus the height of the tallest mountain [I use 100,000 meters]). My camera always looks at a spot 1 meter in front of its position. Once you are dealing with positions up in the millions (about 6.6 million), the accuracy is lost and so it doesn't always register that 1 meter difference.
I found an article online where someone was having similar issues with having the sun at the origin and having the camera out at Earth's distance (about 150 billion meters = 1 AU). He fixed the problem by always making the camera situated at the origin and just positioning all objects based on the camera position. I thought I would give that a try.
I didn't have translation code for my planet yet, so I had to first write that and get it debugged. Once I had that working, it was pretty simple to switch the coordinates around (I added 2 lines of code and commented 1 out). Now my camera works perfectly even when dealing with a planet with a radius of 6.5 million.
I also managed to tweak the Z-fighting occuring with the depth buffer. So it looks alot better than what it did, but it's still not perfect and there are still triangles fighting with each other on the horizon. As soon as I have that fixed, I'll post some more screenshots.