The country's ongoing widely discussed problems are hopeless.
The country's ongoing widely-discussed problems are hopeless.
It is an expensive well-designed program.
It is a well-designed expensive program.
We need a hyphen after widely to form the adjective widely-discussed.
The terms ongoing and widely-discussed are coordinate adjectives, and we should have commas to separate them. As for the order, I feel having the former first sounds more natural.
Similarly, expensive and well-designed are coordinate adjectives; I feel expensive, well-designed sounds better than the reverse. I suggest
The country's ongoing, widely-discussed problems are hopeless.
It is an expensive, well-designed program.