The original novel and movie took place during WWII. The play now takes place during the Gulf War, but it doesn't lend itself to modernization. Kiefer Sutherland does a credible job as Captain Queeg, but lacks the depth that Humphrey Bogart gave to the character in the original movie. Jake Lacy, however is a bit shallow in his characterization of Lt. Maryk. I liked the acting by Jason Clarke as Barney Greenwald, but the gray hair on a fairly young Navy Lieutenant was a bit too much. I also thought Monica Raymond's portrayal of the JAG prosecutor was over the top. Yes, prosecutors have to be zealous in their duties, but...
Quartermaster 3rd Class Urban's character was clearly miscast. First, while it's not unusual for a 20-year-old to be an E-4, it would be virtually impossible for a sailor of his age to have been in the Navy for four years.
Now, to the makeup of the officers on the board. As far as I can remember, flag officers do not serve on courts martial boards for decidedly junior officers. Dale Dye's portrayal of an "Admiral Dewey" was not only farcical, but his uniform decorations were way over the top. There were also several incidents where Navy uniforms were not worn properly, although I can imagine that the short shooting schedule was a major cause of continuity errors.
Navy courts martial don't have Chief/Senior Chief Petty Officers as court MP's. Those duties are handled by U. S. Marines, especially at larger Naval facilities.
In all, the entire play would have been much better had more time been taken to "get it right".