In the course of is wordy for during, in, over, or while. There are rare instances in which in the course of is appropriate (especially when course is meaningful or denotes an actual route or path), but in most cases the phrase could be shortened to a one-word equivalent.
Examples
In each of the following sentences, in the course of could be shortened with no loss of meaning:
But tension returned quickly, and in the course of [during?] their argument, Rick called her out. [Atlantic]
More than 230 western troops were killed in Afghanistan in the course of [in?] 2007. [Guardian]
There’s plenty of interesting stuff to see in the course of [while?] doing that. [AV Club]
The humpback males rapidly adopted a new tune, taking it to the top of the chart in the course of [during?] one breeding season. [Sydney Morning Herald]