When Will first visits April in her apartment during the Bill Clinton 1992 New York primary campaign, April plays "In Spite Of Me" by Morphine (followed by Nirvana's "Come As You Are"). "In Spite Of Me" wasn't released until Morphine's September 1993 album Cure For Pain.
In a scene just after the 15 minute mark, when Ryan Reynolds' character first arrives in New York in 1991, as he passes by the TGI Friday's on Eighth Avenue, a white Mercedes-Benz CLK convertible (W209 model) drives by, which could have been manufactured no earlier than 2003.
At the beginning of the movie, Will is narrating and says that his favorite days are Tuesdays and Fridays because he leaves work early to pick up his daughter Maya from school. (This particular day is a Friday, evidenced by the fact that Maya does not go to school the next day.) When Maya's mom is taking her home from the park the next day, Will says, "See you Wednesday," but he should have said "See you Tuesday," unless he and Maya's mom changed plans.
When Will and April are smoking outside Two Guys, April's cigarette constantly switches from her right to her left hand depending on camera angle [facing her, left hand; facing Will, right hand]. Same thing with her hair in her apartment on the couch with her hair [framing the left side of her face, framing the right].
Will is sitting outside a small restaurant. Just before Summer's surprise reappearance, the waitress serves him his wine and asks him if he has made up his mind yet. At his place is a sandwich with fries etc, just barely started.
When Will goes to visit Summer, Hampton opens the door with his glasses hanging partly under his chin. He adjusts it correctly and then invites Will in. When they're inside the apartment, Hampton's glasses is crooked and under the chin again.
When Will and Summer are called to the hospital, a nurse tells them that Hampton has suffered an "aortal rupture." In medical terminology, all terms relating to the aorta are "aortic". There is no such word as aortal. Notwithstanding this, an aortic rupture is a life threatening condition. Anyone who has this would either be dead or in the Intensive Care Unit heavily sedated, not conversing easily like Hampton was. At the very least, he should have had a blood transfusion bag hanging over his bed.
When Will runs up the stairs in the New Yorker Hotel we see he is staying on the 7th floor. Emily enters the lift bank on the right hand side of the lobby; those lifts go straight to the 20th floor and above. She could not have reached the 7th floor before him using those lifts.
Everything we see of the events that happened in the early 1990s (his first contacts with Emily, April, and Summer) is Will's recollection of how things happened. Since Will is retelling the tales of events that happened many years previously, how the events played out and any anachronisms (e.g. what people were wearing) is subject to the fallibilities of human memory.
During the scene where Will and April are smoking outside the store we see that Will's cigarette has a white filter. Will bought Morley Reds, which is a fictional brand used in movies. The pack has the appearance of Marlboro Reds, which have always had brown filters, leading some people to think his cigarette was a goof.