Some thoughts from learner, who as usual is not sure if what he´s talking is true but maybe you´ll still find it useful 
One use of -mış which I´ve heard of is that it is used for inferential past tense - when you´re talking about situations about which you´ve heard that occured, or which apparently occured, but which have not been witnessed by you directly.
An example from Lewis´ "Turkish Grammar":
A: Geçmiş olsun, evinize hırsız girmiş.
B: Girdi, dedim.
Which means:
A: I hope you soon get over it; I hear your house has been burgled (speaker did not witness it, they have only heard about it).
B: Indeed (lit.: in fact, burglars entered it), I said. (speaker confirms that it indeed happened).
This made me think... because, we can´t be sure that speaker B have witnessed it as well. So maybe -mış tense is used when we want to indicate that we´re not sure about it, while -di tense is used when we want to stress that we´re certain that something had happened?
Edited (9/9/2012) by tomac
[some ugly typos...]
Edited (9/11/2012) by tomac
[Removed my example - too unsure about it]
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