Reckon = I would have said that the phrase should have been "a sight to be reckoned with". This means that it's something that has to be faced potentially with some difficulty. We call a daunting thing or person "a force to be reckoned with".
Angelic = like angels! I think the writer means that the people who use those busy commuter trains and get on/off the train at the most popular stations must be like angels, to have the patience and ability to deal with such a horrible situation.
- For Teachers