Dart

Just banging strings together again. Simple enough once I understood that the original reflection may also be valid after desmudging. I don't know if we were supposed to do something clever for part two, but my part 1 was fast enough that I could just try every possible smudge location and part 2 still ran in 80ms

bool reflectsH(int m, List p) => p.every((l) {
      var l1 = l.take(m).toList().reversed.join('');
      var l2 = l.skip(m);
      var len = min(l1.length, l2.length);
      return l1.take(len) == l2.take(len);
    });

bool reflectsV(int m, List p) {
  var l1 = p.take(m).toList().reversed.toList();
  var l2 = p.skip(m).toList();
  var len = min(l1.length, l2.length);
  return 0.to(len).every((ix) => l1[ix] == l2[ix]);
}

int findReflection(List p, {int butNot = -1}) {
  var mirrors = 1
      .to(p.first.length)
      .where((m) => reflectsH(m, p))
      .toSet()
      .difference({butNot});
  if (mirrors.length == 1) return mirrors.first;

  mirrors = 1
      .to(p.length)
      .where((m) => reflectsV(m, p))
      .toSet()
      .difference({butNot ~/ 100});
  if (mirrors.length == 1) return 100 * mirrors.first;

  return -1; //never
}

int findSecondReflection(List p) {
  var origMatch = findReflection(p);
  for (var r in 0.to(p.length)) {
    for (var c in 0.to(p.first.length)) {
      var pp = p.toList();
      var cells = pp[r].split('');
      cells[c] = (cells[c] == '#') ? '.' : '#';
      pp[r] = cells.join();
      var newMatch = findReflection(pp, butNot: origMatch);
      if (newMatch > -1) return newMatch;
    }
  }
  return -1; // never
}

Iterable> parse(List lines) => lines
    .splitBefore((e) => e.isEmpty)
    .map((e) => e.first.isEmpty ? e.skip(1).toList() : e);

part1(lines) => parse(lines).map(findReflection).sum;

part2(lines) => parse(lines).map(findSecondReflection).sum;