Factual error: When Forrest and Lt. Dan first try catching shrimp on the new boat in the mid 70s, they catch a bunch of junk, including a Mello Yello can, which wasn't launched until 1979. (01:30:05)
Suggested correction: The time frame is right on track. It took Dan a lot of years to get to the point where he joined Forrest on the boat. 1979 tracks with what comes before and after.
You should watch the film again. Hurricane Carmen, which happened after Lt. Dan joined, and they were struggling to catch anything, was in 1974. And Forrest leaves the shrimp business in 1975 when he finds out his mother is dying of cancer. 1979 comes well after all those events. Not to mention that it's only 1981 when Forrest is sitting on the bench telling his story.
Continuity mistake: At the beginning of the movie, before meeting Jenny, Forrest is sitting on a bus bench wearing the Nike shoes he received from Jenny and ran across the country in. When he arrives at Jenny's and crouches down to meet little Forrest, he's wearing brown loafers.
Suggested correction: It's certainly possible that he brought a nicer pair of shoes in his suitcase to change into when he arrived to her place.
Except nothing in the film suggest he had a chance to change shoes. He was so excited to see her and when he found out he's only 5 or 6 blocks away, he runs all the way to her apartment. It wouldn't be in his character to then stop and change shoes before knocking on her door.
If we look closely, those are just dirty shoes. Same ones Jenny gifted him.
Of course it would be in his "character." Forrest Gump was always a tuck in your shirt and straighten your tie kind of guy.
Factual error: In the scene where Forrest Gump is wheeling Lt. Dan across a street between a bunch of taxis, the car they go behind is a 1973 Chevrolet Caprice (see the tail lights). However, several scenes later we know the year is 1971 because it is New Year's Eve 1971 because we see the TV flash 1972 as the year changes. (01:13:30)
Suggested correction: 1971 to 1976 was the second generation of these automobiles, with production of these models beginning in mid-1970. This car would absolutely have existed at the time depicted in the movie.
Factual error: There is a modern 1960's car in the background when Forrest says Bubba's grandmother cooked shrimp. As young as his grandmother appears to be, no such car would have existed at that time.
Suggested correction: Bubba's grandmother is never seen. The person we see serving shrimp is Bubba's mother and then it skips to his great-grandmother.