Great questions. I've seen these suggestions in other places but I'll list the ones I find particularly attractive:
1) Voting in person on election day should be the primary method of voting for 99% of eligible voters.
2) Absentee votes may only be counted if countersigned by a notary public or if originating on an oversees military base. The notary must personally witness the voter signing the envelope and may be charged in the case of fraud, etc.
3) All voters must be full citizens of the United States for at least three years and must show positive ID in order to vote.
4) Welfare recipients surrender their right to vote when they receive government assistance. Anyone discontinuing assistance must wait at least one full year (and pay taxes) to register to vote.
5) Those who do not vote at least every four years are removed from voter registration lists. Voter registration must be an opt-in process.
6) Secretaries of State are criminally liable for maintaining 99%+ accurate voter rolls.
7) If a State decides to implement digital machine counting, the State may not contract that service out to or purchase tabulating machinery from any company which is owned - even partially by or as a subsidiary of - a foreign national. In addition, corporate officers may be held personally and criminally liable if their machines are not accurate to .1% of the overall vote.
8) Random sampling and hand-counting shall take place at every voting precinct with those tallies reported back to the respective Secretary of State for use in giving an accuracy estimate to the People.