Your comment on the incongruity of the same person running the election as administrator and running in the election as candidate (And the Winner Is ... Me, New York Times, October 17th. 2006. A 22) touches only the tip of the iceberg of needed reform.
Most other jurisdictions in democratic societies separate the administration of elections from partisan influence. The Chief Elections Officer, who runs the elections, assigns staff and voting machines to precincts, and counts the vote is a Civil Servant subject to the discipline of Civil Service regulations and not beholden to any particular party. This is not the situation in most of the States in the US where the person responsible for running the election is usually a functionary of the political party in power. This has to be changed.
Second, we must move toward a system of campaign financing that depends on public funding rather than private donation. This last will be difficult to achieve because of the Supreme Court rulings that financial donations to politicians and Political Action Committees are protected by First Amendment free speech provisions. To undo this a long run strategy of a Constitutional amendment will be necessary. One step in the right direction can be achieved by a change in a totally different arena: licensing radio and television stations. Most money in election campaigns goes to a media blitz. If TV and Radio outlets were required, as they are in the UK and Canada, to provide access to political candidates then the necessity for candidates to advertise would diminish. Congress should take the necessary legislative action so that new rules can be in place for the next round of license renewals.
Third, as we have seen in Texas and elsewhere, Electoral Districts are often drawn by the legislature. Districts designed by legislators are meant to do two things: first and most important, to protect and enhance the opportunities for more seats for the majority party; and second to protect incumbents of any political stripe. Often the two major parties will horse-trade boundary lines to protect each other's incumbents. In most jurisdictions outside the USA and in some exemplary US States, redistricting is handed over to an Independent Redistricting Commission. These usually have bipartisan representation on the commission but are independent of the legislature.
These three changes will help restore democracy in the United State.