Other mistake: There is an Ohio flag flying outside the hotel where they're going to play their big gig. (01:33:22)
Suggested correction: This isn't a mistake. The Ohio flag is one of at least 5 flags flown in a row, presumably the others being state flags. And this shot was filmed in Illinois, not Ohio. It's not uncommon for a place to fly multiple flags.
Revealing mistake: During the mall chase scene, a cop car flips upside down and is sliding. At one point, the wires pulling it are briefly visible.
Visible crew/equipment: In a quick, wide shot of the front of the building at the end of the movie, as the cops are trying to break in, the camera and crew are reflected in the back window of the cop car closest to the camera.
Character mistake: When Elwood tells his boss he is going to quit, his boss tells him he will call payroll and have them get his severance pay ready. While employees who resign do have final pay prepared (pro-rated pay, vacation pay, time owed in lieu, etc.) it would never be classified as "severance pay" if the employee resigned on their own accord. Severance pay is classified for employees who are terminated without cause, meaning no fault of their own. (00:43:10)
Suggested correction: This isn't entirely accurate, only what is most common. First, severance pay is not required by law, nor is paying for accrued PTO, so it's at the discretion of employers who can offer it to whomever they wish. An employer may offer a severance package for termination (with or without cause), retirement, or resignation. Often a severance package comes with certain conditions, such as the employee won't seek unemployment or work for a competitor, or may simply be money paid for PTOs.
Suggested correction: This never happened in the movie, Elwood didn't have a job.
Continuity mistake: At Chez Paul when the sommelier is filling Elwood's glass with champagne, he begins to pour and does so again after the cutaway.
Continuity mistake: When the Blues Brothers are paying the assessment in the Cook County Assessor's Office, the area behind the assessor has a desk and is not very wide. In the shot where the camera has panned out, it shows a much larger area behind the assessor. Additionally, how did all of the emergency services personnel get in the room without anyone in the shot seeing or hearing them. When it cuts to this scene, the Blues Brothers look surprised, but they should have easily seen and heard this. (02:18:44)
Continuity mistake: Throughout the "Everybody Needs Somebody" song number, pay attention to the band member in the background smoking a pipe. More specifically, watch the smoke coming out of his pipe. Sometimes it's consistent from shot to shot, but at other times, it changes completely. (Ex. When Jake sings "When my soul's on fire," all of the smoke disappears between cuts).