1. How about having public speeches and texts translated into some of the major languages in the US today, or have simultaneous interpretation at political debates? Spanish, Chinese, Amharic, Italian, Korean, etc. People will never exercise their right to vote if they do not feel included in the outreach process, and one way to solve that is to make the political/campaign process a two-way street by acknowledging the truth that not everyone who is able to vote in this country is fluent in or understands English. If a politician is really about uniting citizens, s/he needs to step up and show the initiative to include all in the conversation, and what better way than by including language access.
2. I'm not sure about the plausibility of this, but I would love to see the voting days moved to the weekends. Having them during the week is outrageously inconvenient for many workers who do not have the luxury of taking time off or away to go cast their votes, whether it be primaries, general, or local elections.
3. YOUTH VOTE. Big, big untapped resource, of course. How to engage a disillusioned and apathetic youth population? Make politics transparent. The transparency bill was a huge step, but that doesn't really engage them. Always foolproof - use what the youth like to emulate, which is nowadays sadly the entertainment industry. Look for cross-initiatives that can be taken with Hollywood or entertainment partnerships that promote political and civic education by having stars hold voter registrations, or having contests/competitions like American Idol but along political or public service lines.
4. Make a lottery. I'm sure if we added a raffle-like million dollars lottery for election days (so whoever votes has a chance at the American dream pie), the turnout would double for the chance to win a million dollars. How closer can you get to the American dream? I kid.