When Milo/Thomas begins falling from the trellis he is holding on from the front; when we see him next he is straddling the trellis from the side.
While the "guardian angels" are supposed to be invisible, they cast shadows. However, the shadows are obviously invisible as well, since no one but Thomas reacts.
When the school-age Thomas goes to the boys room, and comes out of the bathroom stall and goes to wash his hand, he doesn't push on the faucet button to start the water flow, and yet he is "washing" his hands
The trolley poles of the trackless trolley are clearly not making contact with the wire in certain shots.
It is established that the four souls stop appearing to Thomas when he is seven, which would be in 1966 or 67. However, there is a poster drawing on his bedroom wall of John F. Kennedy, Robert F. Kennedy and Martin Luther King Jr. Those posters did not start to appear until after King and Robert Kennedy had both been assassinated in 1968.
Mr & Mrs Reilly were shown about to give birth in a 1958 Rambler. Their interior headshots displayed adjustable headrests in velour - not available in 1958.
Penny Washington is wearing miniature earphones when she's on the bus in 1959, but these were not available until the 1970s.
The bus is driving down Turk Boulevard in San Francisco when Milo boards 1959, however the the wires used to power electric trolleybuses like the one used in the movie weren't installed on that street until the early 1990s.