After Jack's truck is blocked in, he and Lucy both have to walk home from Peter's apartment. But we know from earlier that Peter's car is parked at his apartment and Lucy has the keys. They could have used Peter's car to get home.
When Jack and Lucy are walking by the riverfront and Jack tells Lucy she needs a better coat, they are close to the kissing couple by the light post. As the camera zooms in closer their position changes further back on the sidewalk. They reach the kissing couple for the second time about 30 seconds later.
There are three scenes filmed in the ticket booth - two without bars on the window (in the beginning of the movie, when Lucy is looking dreamily at Peter and in the last scene when Jack proposes to Lucy) and one scene with bars on the window (when Mary and Beth come to visit Lucy)
Lucy is in her apartment taking down the Christmas tree and Joe Jr. knocks on the door. When she goes to answer the door she walks past the globe on the shelf and it is illuminated. When she invites Joe Jr. in and they walk past the globe, it is no longer on.
When Jack and Lucy go to Peter's apartment to deliver furniture, the chair Jack made is strapped to the side of the truck when he opens the truck door. However, when Lucy steps up into the truck and sits in the chair to "test rock" it, it rocks freely and there is no strap.
In the scene at the party where Jack tries to stop Lucy from drinking spiked punch, she puts her hair behind her ear at the start of the talk about the punch, but in the cuts that follow, it alternates between being behind her ear, and covering her ear.
Saul asks the nurse if there is a pharmacy in the hospital, to get Elsie some Nitro for her heart. Hospital pharmacies are usually only for in-patients, so visitor's can't get so much as an Ibuprofen from them. Also, if the hospital did have a pharmacy for out-patients, Saul could not just go down and get Nitro, he'd need to have Elsie's prescription with him.
It is clear that Peter and Lucy's wedding takes place very soon after Peter wakes up. Catholics in America take six months of preparation before a wedding to ready for marriage. Unless Peter and Lucy were marrying outside the Catholic Church, their wedding would not have been performed so soon.
When the Callahans are in Mass, the priest prays for the sick, including Peter. Then everyone sits down, the priest says some more things and the people say 'Amen.' In the Catholic Mass, people don't sit down at that part until the priest has finished the prayers and the people have said 'Amen.' Also, one of the old ladies says Mass was better when it was in Latin and people couldn't understand it. Not true: people had Latin-English Missals and could follow quite easily.
While on the tracks Lucy tells Peter that the train coming toward them is an express, then the train comes to a stop.
However, the train sounds its horn as it approaches Peter & Lucy on the tracks, indicating that they are seen by the driver. Even though the two are not hit, the near miss would have required the driver to stop the train.
The monitor in the ICU shows Peter's blood pressure to be 29/11, not sustainable for life and his heart rate is 80, too high for a coma. The line showing his heart rate is also flat which is what happens when the heart stops beating.
At the end of the movie, after Lucy has told the family she's been lying to them, she leaves the church and the camera pans back to the family. Before Lucy left, Jack was gazing at her from the front of the church. After she leaves, he is gone, not standing next to his brother as he had been moments before.