Question: I am an editor for a trade publication with 40 years of experience in journalism. The company wants me to take a job on the events side, writing content, helping with organization, moderating panels, archiving video. They haven’t called it a promotion but it would clearly be more intense work and involve traveling to conferences every other month. I’d like to accept the offer but I want to negotiate a salary increase after a six-month review. Can I do that upfront or do I wait the six months and in either case, what kind of percentage would be equitable?

Answer: 
You are playing well above your pay grade. Let your manager manage your colleague. An outcome like "the project got finished but wasn't great, one of the interns worked hard but the other was a nightmare" is common as dirt in this industry. 

Do the tasks your manager has assigned to you. When you're out of tasks, go ask for more. When you can't do something because you're waiting on the colleague, let your manager know. When you get something from your colleague and it's unusably bad, ask your manager whether you should fix it up, or bounce it back explaining why you can't use it. Then ask what you should do next given that you can't do what you were planning to do (use the thing from the colleague.)

You seem to think that if you can't fix this other intern (or arrange for a firing) it will reflect poorly on you. Do you really think your manager is so terrible as not to see what you see? You've reported it, shown the code, the manager has already started dealing out tasks and telling the other intern to use source control, and so on. This is all the manager's job, not yours. Relax and do yours, keep your manager informed, and let the manager manage.
Since you are using a versioning system: Fix one bug in his code and check the fix into the versioning system. Then fix another bug and check the fix into the versioning system. And so on. So when you need evidence you point your boss to the versioning system, which contains your name 99 times and his name once.

(In a professional environment with experienced developers you use a source code control system in a different way).

And consider that many companies use an internship as a very, very long interview. If that is the case in your company, then by the sounds of it you are passing the interview, and your colleague is not.