"Spikes" are created when I add a sub surface modifier to my model, even though everything in edit mode seems to be alright Just like my title says, I add a sub surf modified to my model and I get these weird spikes. Its like an intersection gone wrong but I am not sure what is going wrong and what I should even be looking for... Lots of 3D experience, but very little Blender experience.

I was having trouble with duplicate edges just before this started happening, so I deleted all of the bottom edges and started over. Its built pretty simply so I am not sure where its going wrong... Quite simply I just want the bottom edge to be smooth, so that is my ultimate goal.

Also, on a side note, not sure what the red lines are around the other bottom edge. I believe it is a bevel or fillet of some sort but I don't remember what I did to get it on there...

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To remove the spikes press  Space  search for "remove doubles" then hit  F6  to open the setting popover and adjust the merge distance to something like 0.03 to merge vertices that are very close to each other. That should take core of the spikes

Your main problem is that the overall topology of your mesh is not ideal for subdivision. For clean subdivision your model should be predominantly quads.

There is a good article on different types of modeling by Gleb Alexandrov that you can view Here