Throughout the creation of my 2D game I have naturally been creating my own game engine. Now I know if you guys took a look at it you would probably say it is awful. My question is, does this matter if the game is stable and has good performance? I beat myself up over how for example the organization of my engine can be improved. I could make it more understandable and simpler if I took the time to do so, but it would take a while. I keep telling myself that on my next project I will do a complete overhaul and improve it.

I think you would be surprised to see the codebase of some game projects from major companies. They too, suffer from organization issues, hacks, etc sometimes. I think if the game is stable and has good performance, it's okay. But what works for one game doesn't necessarily work for another... and bad code organization can lead to dead ends or having to jump through hoops to achieve what you want... As long as you know what's important to improve and take the time to do it, I think you'll be okay.

My thoughts on the matter can be easily discerned in this thread (through three or four large posts I wrote).

However, if your project is close to completion, you might as well complete it and start with a new blank slate on the next project.
If you haven't read it yet, I'd also recommend Code Complete: 2nd Edition.