As a lecturer, can I use the same problems used in another course in my own course? I will be teaching a new course for the first time.
Fortunately,
I found a massive open online course (MOOC) on edX
which is similar to the course that I want to teach.
However, the difficulty of the MOOC is significantly higher than
the level of the students at my institution.
Consequently, I will be teaching
4 basic topics which I will develop own my own,
in addition to 4 topics which I will adapt from the MOOC.

For the 4 topics which are covered both in the MOOC and my course,
I am thinking of using some of the same or similar material
(e.g., ideas + slides + assignments) from the MOOC.
There are two advantage's of this approach:
It will lessen my workload,
but also reduce the chance that something will go wrong.

Are there any (copyright / ethical / other) issues with this?

Edited in response to comments


[Karl] claims that "There's surely nothing wrong with borrowing some problems like you say in your original question, but just using a complete existing course is very low. How big do you think the chances are you will have time next year to put more work into it?"

I have edited my question to make it more clear that
I am adapting the existing MOOC rather than copying wholesale.
However, is there a problem with using very similar material
for the topics which are covered in both the MOOC and my course?
Brian Borchers
mentioned one potential problem which is
"that students can find solutions to the problems in the MOOC and submit them in response to your assignments. Mixing up the sources of your questions is one way to stop this kind of cheating."

To complete the assignments,
I will ask the students to submit both the code as well as the answers.
I could also change some of the problem parameters
so the answers are not found directly in the MOOC.
Check if the MOOC has a license assigned to it. If it is for example Creative Commons Attribution (CC-BY) you are allowed to use the questions as long as you give a reference to the original creator. You don't need to ask the MOOC in this case. CC-BY-NC (non-commercial) might be a difficult case, because you teach this course as a business and earn money for it. 
A second option is to directly ask the MOOC creators. 
Adapting the question significantly is a third option, as long as you don't copy directly texts from the original question and just base it on the general idea this would be fine.