Listening difficulties

Difficulty

Should students listen to complex spoken texts, or should input material be carefully graded?
Yes, they should listen to the whole text. It's just the question of what information(answers) to be found, so the point is to use grading in difficulty of the listening tasks - at the beginning they must be very simple, and become more and more complicated as the level of knowledge rises.

Speed

How can we help learners to cope with fast speakers?
If the situation happens in real world, we can always ask for slowing down. But generally, the teachers should use normal speed in the classroom ,then there won't be a problem at all. And listening to radio(songs), podcasts, watching TV or having a Skype friend can help greately.

Context

How can we help students to understand the context in which the spoken text occurs?
Using/doing pre-listening activities helps a real lot. This question has already been discussed in Beliefs about teaching listening forum. The link is here.

Accent

How can we overcome the problems posed by speakers' accents?
I see the solution in constant practice - the more you listen the more you understand. And learning about rhythm and sentence stress is also a vital part of it.