If Sarge fought in Korea, even assuming he was barely 18, he would be closer to 80 years old in 2009, more like the grandfather of the bride. Instead he looks like he's in his early 50s, so maybe he was born around the time of the Korean War, but not old enough to have fought in it.
Regarding the smoke from the Cadillac's front tires, the car is a Cadillac Eldorado somewhere between a 1971 and 1978. Beginning with the 1967 model year, all Eldorados were front wheel drive. They shared the same drive train as their sister, the Oldsmobile Toronado.
Sergeant Major is supposed to be a Marine Staff Non-Commissioned officer, but uses the Army's "Hooah" response, rather than the Marines' "Oorah" (equivalent to Navy's "Hooyah"). Similarly, his nickname "Sarge" is an Army or Air Force term, Marines are very insulted by it.
During rehearsal, when the bride and groom are facing each other, they're told by Sergeant Volkom to turn 180 degrees. They do however turn 90 degrees, facing the room (as they should). Had they in fact turned 180 degrees they would of course be standing back to back instead.
Melanie compares Connor to the Tin Man of The Wizard of Oz, saying he was born without a heart, implying that this was the Tin Man's condition. However, the Tin Man's backstory (revealed in the book but not the film) explains that he was once an ordinary human, who had to be rebuilt as a "heartless" Tin Man after his body was destroyed in an industrial accident.
During the initial scene where Sergeant Major Volkom meets Connor Mead, Volom complains there were never any films made about the Korean War. This is incorrect. There were numerous films made, including a major Korean-made film released in the USA. (Four American-made Korean War films were Pork Chop Hill staring Gregory Peck, The Steel Helmet staring Gene Evans, Fixed Bayonets! starring Richard Basehart and Gene Evans, and MASH with Donald Sutherland, both the inspiration for M*A*S*H and based on a book written by an in-theater MASH doctor. The major Korean-made film released in the USA was Tae Guk Gi: The Brotherhood of War. As a veteran of the Korean War, Sergeant Major Volkom would certainly have been aware of at least the first film, "Pork Chop Hill" (1959). As an actor who has been in the business since 1962, Robert Forster himself may even have been aware of the Gregory Peck film.)
He also states the war "lost more men than 'Nam." Actually, it was around 2,000 less.
When Jenny is trying to piece the cake back together while talking to Brad, the amount of frosting on her fingers changes during shots. Sometimes they are completely covered, and other times there is hardly any frosting on them.
When Connor goes to his prom dance we can hear "The Safety Dance" by Men Without Hats setting the action after 1982. After the prom, Connor goes to with his uncle to a place where we can hear "Get Down Tonight" by KC & The Sunshine Band (released in 1975). Approximately two years later, Connor says "I got the new Poison," and shortly thereafter, "Nothin' But a Good Time" (released in May 1988) begins playing. Therefore we can assume that the dance was in 1986 and there were no anachronisms present.
When young Connor and Jenny are shown together in 1982, he says his parents died a year later. However, later in the movie his brother says Connor was 7 when his parents died which would have made he and Jenny 6 when they were on the swing and she gave him the camera. The actors are clearly much older than 6. Maybe 11 or 12.