It seems everyone is talking about process at the moment, whether it's broken or not. Since I've been playing with HTML, then CSS etc etc my process has adapted. From being taught in college to draw out the site map before anything else (back in 1998) everytime I've come to create a site be it designed and developed by myself or, more recently, designed by others to be coded and 'responsified' by myself I change 'bits' of how I work.
I can't tell you really what they are, I don't write enough things down.
But I'd say my process is broken, it will never be perfect. Life moves pretty fast for the chance to have a correct, 100% working process because I'm always learning and trying new things.
Always Be Changing.
And, I'm happy with that. It works, it could be better, but it works, for me and clients I have work(ed) with/for. Some tools and ways or working continue project to project, possibly being refined, so slightly, each time. Things like pre-processors and how I use them have forever been in a state of flux since i first started using LESS and more recently moving to Sass/SCSS.
I can't tell you how to change your process, I can't tell the best way to do something in your process. It's your process, used by you. Who, unsuprisingly, is not me. I can suggest just the one thing.
After a project your next project goes out the door sit back, think of all the things that helped and all the things that hindered that project. Write them down (I'm doing this as soon as my client's client gives me things to finish). Think of what you can change, add or subtract to the process you've just gone through to make it better.
Client communication, design sign off, boilerplate starting files, CSS commenting, SCSS mixins, HTML/HAML templates, Photoshop editing, local enviroment development, pushing it to the server, version control and much more. There's bound to be something in your process that you can find that needs adapting, figure how you can make it better and do it, rinse and repeat.