During the scene of Jan's wedding, the person marrying the couple announces "with the power vested in me by the state of Massachusetts." However, Massachusetts is a commonwealth, and any Massachusetts governmental officer would actually say "vested in me by the Commonwealth of Massachusetts."
In this, as in almost all films where an attempt is made to characterize a Boston accent, players don't understand that Bostonians would never not pronounce the r at the end of a word if the next word begins with a vowel. The classic "Park the car in Harvard Yard" is supposed to be pronounced thusly, "Pahk the car in Hahvad Yahd."
Once the other members of the Bella family learn about Sam's relationship with Renata, they all express skepticism about his motives, his fidelity, his purported wealth, etc. Nevertheless, ultimately they all accept him without any intervening activities that demonstrate his trustworthiness.
In several scenes (frozen pants hanging on the laundry line, skating on a lake that's frozen solid) we see deciduous trees with green leaves plus green grass once it's supposedly winter in the Boston area. Also, in several "winter" scenes, we don't see anyone's breath in the cold air.
When Renata is reclining on the bed watching old home movies, then Sam redirects and refocuses the image onto Renata's very-pregnant belly, then we see the projector from the other side of the bed: It's projecting light at a much-broader angle than would fit on her belly.
The goof item below may give away important plot points.
Jan is visibly distraught over Renata's situation, sobbing while sitting on the bed. Renata leaves her daughter, whom she had been feeding in a child seat on the floor, and goes to Jan to console her. While the two sisters are hugging, Jan looks over Renata's shoulder at the baby, who is facing her head-on. Yet when Renata walked from the baby to Jan, and returned from Jan to the baby, the child seat is seen positioned sideways to Jan's line of sight.