"Looking at other countries, such as Sweden that already has free post-secondary education for its students, it would be a good idea for Canada, as a nation, to do the same."
There are two ways to look at this problem, but either way, we need a comma after Sweden. Now, if we take the error to be one of number, all we need to do is to change the has to have to agree with countries and we're done. This is most likely what she meant. But there is another option: change the that to a which and suddenly has now agrees with Sweden.
The reason for this is that countries can be more clearly identified with more information whereas Sweden, being one of a kind, can't. Consequently, when we come to that, we automatically resolve it such that it applies to countries, as that is used only with integrated relative clauses. Which, on the other hand, works with supplementary relatives, making it entirely plausible that the information about free education pertains to Sweden making the relationship Sweden has rather than countries have.