Say someone contributed more than they were allowed to for a Roth IRA in Year 1 (therefore, there was an excess contribution). Can they still re-characterize that contribution to a Traditional IRA contribution between April 15 and October 15 of Year 2?
From the Publication 590 part on recharacterizing excess contributions, the example seems to indicate not:
You contributed more than you were entitled to in 2012. You cannot recharacterize the excess contributions you made in 2012 after April 15, 2013, because contributions after that date are no longer timely for 2012.
However, the sentences above talk about this "If you are applying excess contributions for prior years as current contributions", so it sounds like you could not apply excess contributions for prior years as current contributions, and then it would be okay.
The section on extensions for recharacterizations seems to indicate that it is okay to recharacterize between April and October for the previous year as long as the return was timely filed.