You can only improve by constant practice and listening only to English. This link gives some valuable advice: Listening Skills
You could also look at this one: English Listening Skills and Activities-Effective Listening Practice for ESL EFL Learners and Teachers
With your customers, if they are speaking too fast, try saying "I am sorry, I am afraid I did not catch that. Would you repeat it more slowly?"
Can you give some examples of where you have confused the use of "the"?