More details on how 5 of the 15 problems could be solved when all leaders know that their MAIN MANDATE is just to fix these problems:

Problem #1: Our leaders have NOT done anything effective concerning CAMPAIGN FINANCE REFORM or misleading advertising.

Simply outlaw ALL donations and monitor all political advertising. Allocating much less than 1% of our tax dollars would easily fund all national and local campaign expenses. The money would be available to the top 3 political groups (Republican, Democrat, and the top independent group). This would stop our "buy a politician" problem immediately- AND allow our leaders to stop all of the wasteful fund raising activities that consumes so much of their time. A committee could be appointed to oversee and monitor all political advertising to make sure the facts and  portrayals were accurate and true. 
NOTE: Other political groups not covered by the national funding could be allowed to solicit funds up to a the maximum given to each of the 3 main groups to avoid unequal overspending. Also no advertising would be allowed by supposed independent groups that take no responsibility and often advertise total falsehoods.
And limit the endless campaigning by enacting a law limiting the formal campaigning for offices to just 6 months before the elections (most people are sick and tired of our politicians wasting half of their terms campaigning).

Problem # 2: Our leaders have not secured AMERICA'S BORDERS or enforced our laws on illegal immigration.

SOLUTION: Allocate sufficient money (at least $10 billion dollars), build a complete fence and/or use the latest technology. Send up to triple the troops and border agents and give them the authority to do their job.Then demand/enforce that employers be seriously fined if they hire illegal workers (this alone would actually solve the illegal worker's problem because they would no longer have a job and would have to leave and/or apply for a proper visa just like others who are legally pursuing visas)...Some consideration might be given for length of work, exemplary service, and no criminal record. Then, if  there were still a true lack of workers, we could just allow the free market system to work by paying wages that Americans WOULD work for. This could have the additional benefit of greatly lowering our unemployment rate and increasing wages for Americans citizens which includes all types of citizens- Caucasian, Hispanics, African Americans, Aseans etc. (Once our own unemployment is low again, and if there still were actually not enough workers, we could easily increase the number of legal workers through quest worker programs etc.).
NOTE: We are not against a people; we are FOR Americans. Right now we need more compassion for our own people and all of the job losses, crime, educational deterioration and diseases etc. Also, with the money saved (and those who might be allowed to work here being absolutely required to pay taxes), we could probably even send more money to Mexico so they could start fixing their own country.

Some products and service prices might increase, but this is the price we would need to pay. Also, all American companies would be on the same footing with none having the unfair advantage of illegal cheap labor.
Also, even if some partial compromise were made because of a true worker shortage and with a desire to help some of the long time good workers and their families, it is always important for a person/group to understand that this is a priviledge America is giving, NOT a right that they're automatically entitled to (America must be wiser in it's giving- our country has far too many ungrateful recipients around the world!).
Problem #3: Our leaders have NOT weaned us from DEPENDENCE ON OIL through serious funding of research to develop alternative fuels, AND have not stopped the oil companies from pillaging the American people with their extreme windfall profits.

SOLUTION: Because our transportation system is one of our national interests, we can not be held hostage to the oil companies' corporate greed in this vital area. These companies must be slapped with on-going wind fall profit fines which could be returned to all Americans and also used to fund the Mahattan/Apollo type project of gathering the worlds best scientists to intensively develop alternative technology to finally wean us from our dangerous and expensive oil dependence (this alone would probably do more for the "war on terror" than anything else we have done to date- "let them have their oil and play their games on other oil dependent countries"). Then, if we did develop this alternate technology, our country would have a huge new industry to employ American workers, along with technology and products to export to the rest of the world- to get them off their oil dependence too. This would deal a huge blow to the oil producing dictatorships, and terrorist sponsoring countries (then maybe we could finally, and effectively promote democracies by financially rewarding those countries who agreed to develop true democracies).
Problem #4: Our leaders have NOT taken action to lower the huge BUDGET DEFICIT and TRADE IMBALANCE  (with the understanding that we must first get our economy back on track).

SOLUTION: Wisely, invest more in America's infrastructure, education, and technical areas to increase our productivity and innovativeness. This could greatly increase our national income to reduce the budget deficit. 
Other ways to produce more national income might include such creative methods as partnerships with government and inventors where copy right/patent protection and money could be provided to the inventors in exchange for a percentage of the rights/income. 
Whole new industries could be created by Manhattan type projects like the one to give us alternative energy.

Plugging loopholes for the rich and large corporations could also save us $10's or even $100's of billions.

Inact fair and enforceable trade policies.

*Stopping the ineffective spending and pork barrelling in government (paying taxes is unpleasant enough without having to watch significant taxes being spent foolishly and ineffectively- And there must be accountability and full disclosure!).

Problem #5: Our leaders  have NOT gained control of our EXTREME LEGAL SYSTEM 

SOLUTION: This is one of the more complicated problems which will require passing some common sense legislation/"spirit of the law type" that could help stop many ridiculous and harmful abuses of our legal system and laws which have now often gone to the extreme. We must finally reverse the culture of "suing on anything we can" and changing some of the letter of the law applications, and laws which 
are often abused by special interest groups and other extreme/greedy types. Many of these laws originally had their purpose but are now being abused, and are in need of revision to reflect the new realities. 
This may require something unprecedented, like gathering together 10-20 older "wise men" and women from across America, who could periodically review current realities and help revise our national laws and their applications (courts might also make use of a potentially more just and reliable system where older, mature, and wise men and women would serve as volunteer or partially paid jurors).
Finally, in order to truly improve our legal system and societal practices, and to have true fairness and full disclosure, the all pervasive abuse of hiding behind lanquage and even statistics, that purposely deceive but are "technically" correct, must be stopped and labeled for what it is- a purposeful distortion of the truth, a lie! 

NOTE: Of course, the ideas listed above are not complete or perfect. They do, however, show some relatively simple methods that could be employed to much more effectively address these problems (with strong motivation to really act on these issues, these ideas could be expanded and adjusted to arrive at the most effective methods of solving these major problems). Also, it should be understood that each of these problems has to be solved in a comprehensive and COMPLETE manner. Piece meal, half measures will not work (we've had that approach for decades. It's neither sincere nor effective!). Our vast majority (over 2/3rds of us) must demand and force our leaders to finally and fully fix these major problems.