Currently, approval in the game does not do anything but give others simple ideas on what you are up to. I have a few suggestions to improve this.
You should allow the approval to enter negatives for a start. 0% would be a zone with no effects.
Now, for some effects:
When at high approval, your nation should get bonuses, such as maybe a better economy, or military units being more motivated to fight for you and thus more efficient.
When you have low ratings, you might have higher crime, military costing more, workers in resource making buildings less efficient etc.
This other bit I could go without, but it would be cool if each city had an individual happiness, making them possibly get population faster from people moving there, maybe more money, or something like that. Ways you could help this could be to build parks or carnivals.
Now, some problems and solutions:
Players already have 0%? 0 is the neutral zone, so nothing would happen, they would just need to try had to get higher.
Approval hard to come by? Add more ways! Maybe being promoted and demoted in an alliance could ad or remove approval, or maybe every $1M you get total adds a little bit!
Alex, I truly hope you consider this and think about my suggestion. Some things could use balancing, but overall I think this will certainly help the game be realistic.