When Logan returns home, the highest medal he wears is the Distinguished Service Medal. This medal is generally only awarded to senior colonels and generals, not to sergeants. Also, Logan wears a combat patch and was awarded the Distinguished Service Cross (which is only awarded in war time and different from the DSM discussed above), but does not wear a Combat Infantryman's Badge nor any combat service medals.
The commanding officer briefing the Rangers is wearing a mustache that conflicts with regulations. Mustaches are not to be worn beyond the edge of the lip.
At the very beginning of the film, there's a shot of inner city Chicago. The date is shown as 1983, yet the cars on the city streets are clearly 1990s models.