1. Overturn Citizens United
Citizens United was the 2010 Supreme Court case that has allowed corporations to dump millions of dollars into campaigns, and it has also allowed the formation of multi-million dollar "Super-PACs", which allows corporations and individuals to funnel in money to T.V. Ads/etc. anonymously (tearing apart any aspect of transparency in our electoral process).
Overturning Citizens United is by far the most important thing our country can do to protect our electoral and political systems.
I would also like to see all of our campaigns become publicly financed, but I doubt anything like that could ever pass through Congress. This is unfortunate though because if we pulled the money out of the process then we'd eliminate a lot of the corruption (though not all because of Congress' power over the appropriations process, which is necessary since you want people who can be held accountable by the voters to control that process).
2. Proportional Representation
This is an issue that could actually bring the far left and the far right together, and it would create a system that would be more beneficial for everyone (not just the extremes). Right now we have a two-party system, and within each party (especially the Democratic Party) there are people with many different viewpoints. Therefore, you can only predict to a certain point what you are voting for when you vote for a political party (and a lot more focus is placed on the individual candidate as a result).
As opposed to the single member districts that we have now, if we allowed parties to be voted on for Congress and if we allowed each party to take the proportional amount of seats as compared to the percentage of the popular vote that each party received (ex: A party that wins 1% of the vote would get 4 seats), then we could allow multiple parties to exist. This could be done on a national level, or Congressional seats could be voted on within each state as a whole (I would prefer it be done on national level since that would be more in line with 1 person 1 vote...it would be more proportional).
Result: We finally get rid of the dreaded Congressional gerrymandering of districts (one of our political system's greatest illnesses), and we finally get multiple parties. The significance of having a multiple party system is consistency. You can actually know what to expect from a political party. Don't get me wrong, I am one of those who actually realizes that there are gigantic differences between the two parties (I'm so sick of the ignorant statement: "Both parties are the same"...read the legislation they propose for 5 seconds and you'll see there are some gigantic ideological differences); however, I also realize that there is ideological diversity within the parties and this causes more voter confusion than anything else. If green, libertarian, and other third parties were allowed to exist, then people could know exactly what platforms they are voting for when they cast their ballot. This would create more trust between the public and the government, and the business community could actually know what to expect from the government in power at the time (business loves stability in government).
3. End the Electoral College
This may actually be carried out by National Popular Vote (nationalpopularvote.com) before a Constitutional amendment could be ratified. What National Popular Vote is doing is basically lobbying state legislatures to pass legislation that would cause the states who agree to give all of their electoral votes to the candidate who wins the national popular vote. However, states would not have to do this until enough states pass the legislation to make up a majority of the electoral college (270...they are currently at 132, which includes VT, MD, WA, IL, CA, NJ, MA, HI, and D.C.).
However, I still think it is worth bringing this up here since it only makes sense that we allow the nation as a whole to elect our President (as opposed to allowing a handful of battleground states to elect our President). This issue also has more bipartisan support than the other two issues I brought up above. People on the right and the left realize that its unfair that Democrats in TX and Republicans in CA, both of which are large groups of people, hardly have a voice when it comes to Presidential elections.
4. Getting rid of or at least modifying the filibuster/unanimous consent rules in the Senate.
This would probably be a given if the rest of the above proposals were to pass, and this is also something that would not require a Constitutional Amendment. The filibuster and the other procedural rules are not given to us by the Constitution. They are given to us by the tradition of the U.S. Senate. One of my law professors once convinced me that we should keep the procedural rules of the Senate intact since they force compromise, make sure that any change that is made in our country is a baby-step as opposed to a leap forward, and that business loves the stability that this type of process creates. However, I have since been convinced that this process has been broken by a political party that refuses to compromise. Maybe I'm wrong, and, after the GOP loses badly in a couple of election cycles, they'll realize that you have to have the middle on your side to win. Until that happens, I'm sticking to my opinion that these procedural rules need to go.
On the first legislative day of every Congress (which usually goes many real days so don't take this as meaning one day), the Senate can change its procedural rules with a simple majority. Senator Udall attempted this earlier this year, and here is the list of his reasonable proposals (quoted from the CNN article linked below):
"Udall is considering four key proposals as part of the resolution he will offer. One would prevent filibusters to taking up a bill or on a nomination, although it will still allow filibusters to end debate on a bill. A second would eliminate so-called "secret holds" in which a senator can anonymously stall legislation or a nomination from coming to the floor. A third would require senators leading a filibuster stay on the floor and debate the issue during the entire filibuster.
A fourth proposal from Udall is aimed at appeasing GOP concerns about being locked out of the process. It would require a certain number of amendments for the minority party for any bill being debated."Here is a link explaining the end agreement that the two parties settled on earlier this year (which resulted in small changes in the right direction as opposed to the bigger/better changes proposed by Sen. Udall):
Here's a more condensed version of the agreement: http://fixthesenatenow.org/news/entry/senate-leadership-agrees-upon-rules-package/
"Senate Majority Leader Harry Reid and Minority Leader Mitch McConnell, reached a mutual agreement on a new procedural system for the 112th Senate, earlier today.
The agreement eliminates secret holds, prohibits delay tactics like forcing the reading an amendment that has already been submitted for 72 hours, and exempts about one third of executive nominations from the Senate confirmation process.
Additionally, Sen. Reid agreed to reduce the use of 'filling the amendment tree,' while Sen. McConnell agreed to limit the number of filibusters. Both party leaders agreed not to seek the Constitutional option to change rules in the 112th or the 113th Congress."
I understand the argument for preserving the filibuster and other procedural rules of the Senate, which mostly evolve around the fear of the Senate becoming the partisan House. However, when one party decides gridlock is better than compromise, its difficult to side with the status quo on the rules of the Senate.
These proposals would not solve all of the world's problems, and we would still continue to have plenty of problems in our own country. However, what these proposals would produce, if they were to pass, would be a cleaner, fairer, and more transparent electoral and political system, which would better represent our country's electorate and would create more trust between Americans and their government.