The first time I saw The Question was on Justice League: Unlimited and he held his own and truly served a purpose. The Question is a very skilled detective that rivals even Batman. Also he is skilled in hand to hand combat not to mention possesses computer skills to break any encryption set on any super computer.
Now that I established he has the skills to hold his own, lets get into the wide array of original stories you could use to present this character to the world. I know he is not box office but he has the same potential that Ironman had when it was released back in 2008. I know Ironman is way more established than the Question but if done right then the franchise could spawn into a trilogy. Another factor that can help make the movie better is the use of current events to tell the story.
The Question is the conspiracy theorist of the DC universe so using such events as 9/11, the Kennedy Assassination, Area 51, or Illuminati could help. The formula for making these movies a success changes a little with every movie made. Everything has been done and redone which makes coming up with something in a movie that will surprise your audience is truly difficult. So coming up with concepts that will get that reaction from your audience is a little easier with a character like the Question.
The Question can leave you asking questions during the movie like who is the bad guy and will he or wont he. Going dark seems to be the theme that DC is going with and this is a character that can do dark but can make you laugh at the same time as well. You can relate to this character, seeing that he has no superpowers and the threats can hit home because he can be taken out with ease just like you and me.
This is a character that has the potential to be just as successful as the John McClane character in the Die Hard series. So in closing The Question is a entertaining character that can help expand the DCCU by crossing paths with characters like Wildcat, The Huntress, Green Arrow, Steel, or Vandal Savage. The possibilities are endless.