I definitely want to get rid of plurality voting, and change to range voting (or reweighted range voting for some offices).
I'd replace party labels on ballots with a space where candidates could summarize their platforms. I suppose party affiliations and endorsements could be included here as well.
I'd provide a space on ballots for individuals to include anonymous petitions to be officially filed in the library of congress. I might require congress to begin with a period in which the only bills that can be proposed are those coming from these petitions rather than the politicians' own ideas.
I'd seriously consider making the oath of office for most elected officials require them to not run for any office until their term is up. This includes running for reelection as well as using one office in order to gain the political clout to run for higher office.
I tend to think that state legislatures should have representation in congress, but the pre-17th amendment appointment of senators is probably not the best way to do that. I might suggest bringing back the Committee of the States, although not quite as it operated under the Articles of Confederation. Each state government could send as many or as few delegates to this third house of the legislature as it wishes, and could recall them at any time for any reason. They would each would control only a fraction of a single state vote and state laws would be able to override them. These delegates would receive no income or benefits from the federal government, only from the states.
The Senate would be made up of representatives from the nation at large, with the whole county being a single multimember district. I'm thinking there would be a senatorial election each year, with the top 5 candidates earning a single 5 year term.
I'd probably allow laws to pass with the support of only 2 of the 3 houses, but require all to agree in order to override a veto.
I'd allow the president to propose bills directly, and make them become law immediately (without wasting time allowing for him to sign or veto them) if congress passes them unammended.
I'd allow a limited line-item veto.
I'd allow congress to overturn any executive order at any time.
I'd require all bills to include a justification stating what in the constitution gives the government the power to take such action.
I'd consider requiring bills to be passed in at least 3 languages, to hopefully minimize the risk of terms changing their meaning and obscuring the intent of the law.
I would create a limited federal level plebiscite. Congress would not be allowed to call any referendum, but enough petitions could automatically place initiatives on the ballot. I would probably not allow laws to be passed this way, as the format does not allow adequate negotiation. Instead, I would allow the public to use these (with a large enough supermajority) to strike down existing laws or executive orders (and maybe even judicial doctrines), as well as to remove any government official from office.
In general I'd want to move towards greater decentralization, but would rather move property taxes (or rather land value taxes) to be mostly at the federal level. I would ban unfunded mandates, and encourage the federal government to run its own programs rather than forcing states to run any.
I would probably get rid of the electoral college, but might consider giving it more power instead. If I took that approach then I would make it function somewhat like the system Lewis Carrol recommended, where electors would treat the votes for them like a resource with which to bargain. Rather than cast one ballot they could go through extensive negotiations before deciding not only on who should be president but on who should be the head of various federal departments. The college would reconvene in order to fill vacancies, rather than leaving this to the president or congress. If electors were retained then obviously we would need to make it so that each elector campaigns for himself and appears on the ballot separately rather than being in an anonymous list associated with one candidate.
I'd ban any official recognition of political parties. The right of free assembly/association allows parties to continue to exist, but there is no reason we ought to imbue them with any special powers. All elections would be non-partisan, and parties could play no role in deciding leadership in congress. Neither could seniority. Instead, congress would rely on range voting for choosing its own leaders too.
I am inclined to make judges rotate through the judicial system rather than staying for life in one district. Moving judges would help make the system more uniform, rather than leaving some circuits more progressive or conservative or business friendly than others.
I would give all members of juries the same rights as the attorneys for either side. They could cross examine any witness and even call in their own experts to testify. I might also require the attorneys to swear the same oath as witnesses, and charge them for perjury if they prevaricate. Jurors would be able to vote guilty, not guilty, or not proven. A not proven verdict would allow a retrial without violated double jeopardy protections, but only if more evidence was uncovered. Jurors would have a say in sentences instead of only deciding guilt or innocence and then leaving that up to the judge or overly specific statutes. Jury nullification would probably be allowed, possibly with limitations. When a jury decides that the law is unjust I might make it automatically place the law on the ballot for review by the populace. If the accused was found to have violated the law they try to nullify his status would depend on the outcome of the plebiscite.
I would at least try to minimize the importance of precedent, and encourage plain readings of the constitution.