My initial reaction is that the students have difficulty listening for gist. Listening for gist involves getting the main idea of the text, an overview of what is being said rather than focusing on specific information. It also involves disregarding any irrelevant information, including “umms and aaah’s” and false starts.
I think it’s excellent that your students are able to catch all the words and they should be complimented on this. However, I wonder whether the listening texts you have used are too easy for them. This is a point for you to consider.
I think you also need to do some work on listening for gist in class. Do this during the first listening of any recording. Depending on the subject, you can ask students to tell you
the main story line;
whether the speaker is expressing a positive or negative opinion;
whether speakers agree with each other.
After this, you can focus on listening for specific information. This involves questions such as:
How much did the meal cost?
Where have the speakers decided to meet?
What time is the film starting?
Etc, depending on the topic.