Just for a change of pace, I thought I'd report on the experience my mother and daughter just had with Delta (yesterday). They were flying from our regional airport connecting in DTW and on to MHT. Inconveniently, due to a mechanical problem, the plane that was supposed to come from DTW to our airport and then take them back to DTW was significantly delayed (by about 3-4 hours), which of course delayed their flight as there was no plane to fly them on. The flight to MHT was also delayed but not as much, so their estimated (and actual) arrival time into DTW was after their connecting flight was estimated to leave.
Delta rebooked them on a flight out of DTW the next morning before they even left our home airport. In fact, they had them booked on both their original flight and the flight the next AM, just in case they got there in time. (Although my mother did have to speak to 2 people before she got someone who knew how to do that.) They also paid for a hotel in Detroit (I haven't determined which one yet, but DD reported that it was "fancy" and was impressed enough to send me photos of the lobby and elevator via text). This seemed to go quite smoothly when they arrived in DTW, as it did not take them long to get onto the hotel shuttle. Delta also offered to rebook their entire flight for today so they could have come home for the night, but my mother elected to get at least as far as DTW yesterday.
I'm guessing Delta flew a different plane out for their flight to DTW, as it was larger and had a different seat configuration than the original. (DD reported 25 people on a plane that would hold 124.)
This morning they arrived successfully in MHT, so are really only out a half day at their destination plus the time spent at the airport.
It's unfortunate that they were delayed at all, but I thought Delta handled it as well as could be expected. It probably helped that I was checking their flights online so my mother knew to go ask for assistance once it was clear that they would be very unlikely to make their connecting flight. The Delta website seems to be pretty accurate for checking flight status, based on comparing what I saw there with the text updates they were sending me.
I'll add that their original connection time was only 1h 8m in DTW which I didn't really like (I'd prefer 2 hours) but the only other option when I booked was 46 min. It's unclear to me if a 2h connection would have helped or not in this situation though, as both flights were delayed.
Just out of curiosity, have there been more delays in DTW lately? Their flight this am was delayed by an hour too, but I don't know why.