[CAUTION: I am not a teacher:take the advice and or corrections offered in this post at your own risk.
If you doubt the information, please get a qualified opinion from one of the teachers on these forums.]
I would try to address serious pronunciation problems on three fronts.
(1)The alphabet and phonetic symbols
Many language learners become quite advanced in reading and writing while retaining only a foggy notion of the relationship between the symbols of English writing and their pronunciation.
For these students they should be introduced to the nuance and difference between each symbol and combination thereof. This can be tedious and difficult, but is necessary to the mechanical understanding of pronunciation, especially if a majority of their ideas about how words should be pronounced comes from writing.
This has the potential to be incredibly boring but is just plain necessary, just like a musician has to learn all the rules of written music although technically she or he may play an instrument without it.
If a native speaker were to go deaf, his or her speaking ability would suffer and decline into near unintelligibility in months. The reason being that they can't hear themselves speak.
I would argue that listening ability plays the first role in our pronunciation with mechanical oral ability coming in a close second. Reasonably, if someone cannot hear the difference between words with similar pronunciation, or their slight mispronunciation of a sound, they cannot reproduce this difference correctly.
A great amount of exposure to the spoken language is required indeed, but this can come from movies or music/songs (books on tape, perhaps?) just as well as speech, and may be more entertaining. Not only this, but I find that stress and intonation tend to be slightly exaggerated in song and performance, and so are easier to pick up.
Not to mention, all language learners I have known with exceptional pronunciation who have not had a lot of personal exposure to native speakers usually watch a considerable amount of television in the target language or listen to music of the same.
(3)Recording one's voice
Easily the most difficult practise to encourage, we all have grand illusions as to the rich and musical sound of our own voice, which are often shattered when we hear it in recording. This is perhaps even more reason to do this exercise.
Some tape and CD players specifically designed for language study provide a function whereby the learner can record their voice for direct comparison with the recorded material, but this can easily be set up by any determined student.
Finally, a consideration for ability.
Like musical ability, some people just naturally show talent for learning the sounds of language where others do not. As native speakers we often ignore the systematically flawed pronunciation of other native speakers but on observation can point it out easily enough.
Some people never even master the sounds of their own language, which is odd. Others do fine with pronunciation of their own language but fail miserably when introduced to a second (Jackie Chan who I revere comes to mind).
Also, we must factor in age, I have heard people who begin learning language in adolescence never completely lose an accent. You might not want to undertake an impossible mission.
Still, movies like "My Fair Lady" and my own personal experience (I started learning Mandarin at 21 and now four years later can fool native speakers on the phone into thinking I'm Chinese. Granted, I spent those years living among native speakers.) show us that exceptions are possible.
I hope this has been helpful.