Tell me if you disagree, but I think the biggest problem with our current political system is campaign contributions. Basically, the problem is that in order to be elected, you have to fund your campaign. Since most funding comes from corporations or special interest groups, politicians become beholden to said corporations or special interest groups and therefore work in their best interest rather than the interest of the public at large. This also encourages extremism in the beliefs of the candidates and what they propose because they're trying to get the support of a group that supports that belief (a problem with the political party system in general).
I can see two ways of fixing this:
1. Fund campaigns using government money.
2. Require all campaign contributions to be anonymous.
Option 1 should theoretically be more effective because each candidate would have an even playing field and voters would support the person with beliefs most in tune with their own. Since candidates run on money from the people, they're beholden to the people, not a faceless entity. Option 1 also evens the power between the wealthy and the poor since campaigns aren't dependent on the amount of money each supporter has available to donate.
Option 2 is more moderate. People, corporations, and groups could still donate to help ensure their candidate wins, but the candidate is theoretically unaware of where these funds are coming from and is therefore less beholden to these groups. However, there is a large potential for abuse by off-the-record phone calls and the like. This option also has the downside of wealthier people having more influence.
Or there is a third option:
3. Allow people to vote on the issues themselves rather than having a representative do it for them.
This would be the theoretical ideal but it runs into the problem of informing people about all the issues in a simple enough way that everyone could understand and then actually getting them to go out and vote. This is already hard for some people and increasing the number of things they're voting for might make it worse for some, though it might make it better for others since they would feel like they're part of the real process and not just voting between bad candidate A and bad candidate B.