I spent 4 years as a Court Officer, part of my job was supervising the Voir Dire (Jury Selection). If picking jurors for a criminal trial; by all means a background in law enforcement will all but guarantee that you will not be chosen. Now for a civil trial, the only thing that the attorneys and judge are concerned with are your ability to listen and weigh all the evidence and be fair.
And by the way no matter how interesting the case may sound it is going to be boring as hell after opening statements
90% of my job was to keep the jurors awake.