You have a couple of options.
You can sue the plumber although there are some issues with that. Since you didn't hire him the judge could say that you have no standing to sue. In addition, there may not be any specific time or dates given to finish the job.
Another option you have is to take the position that this is a "constructive eviction" by the landlord. In a constructive eviction the landlord would be liable for any moving expenses you have, extra deposits, etc. It is a way to get out of the lease and to get the costs covered.
If you want to try constructive eviction you will need to get a lawyer to write a letter for you to the landlord giving them a specific date by which the issue must be corrected as well as warning them if it is not then you will consider it "constructive eviction". You need a lawyer because it has to be worded just right and also because the letter may be used as evidence later and so you want it t be worded in such a way that it sounds better for you.
If your question has been answered then I'd offer my best wishes to you and ask that you please not forget to leave a Positive Rating so I receive credit for my work.
Of course, please feel free to ask any follow up questions in this thread. I want to be sure that all of your questions are answered. In addition, once you issue your Positive Rating the question will lock open and you can come back to it anytime in the future if you think of something else.