When the FBI traces the cell phone which Alistair Peck is using they announce that it is at an address near MIT. However, the computer program they are using shows it's location on a map as being somewhere either in The South End or Roxbury. This is nowhere near MIT, which is located several miles to the North in Cambridge.
When the train is entering the station a loudspeaker announces that it is "Boston Bay Station" and that there are connections to the Silver and Orange lines. There is no Boston Bay Station. There is a Back Bay Station which has both commuter rail and Orange Line service but it doesn't have Silver Line service. There is, in fact, no MBTA station with commuter rail, Orange Line and Silver Line service.
When Peck has his final time jump he draws all the energy around him as evident by the wide arc of dead grass at his landing point. However, the hot air balloon adjacent to him and within the arc of dead grass still has its hot air and its flame is still lit.