I have interviewed with USCG and USAF JAG multiple times and have attended part of USMC OCS (dismissed due to injury).
If you have no military background, one of the first things they will screen for is whether you are suited for military culture. Yes, the USN is not all gung ho military like the Army or USMC, but they do want to make sure you are fully aware that deployments are possible, frequent changes of residence are likely, and that you understand that military culture has certain expectations of discipline that are a bit different than the civilian world.
Beyond making sure you can adapt to military culture (which is basically a pass/fail type of screening), the rest of the interview should not be too much different than a regular legal interview. Much will depend on who is doing the interviewing, as a direct commission JAG on the panel will have much different experiences than a JAG with prior service in the fleet or in another service.
It would be good to highlight leadership experiences that you have had in the past, because as someone who will pick up the rank of O-3 relatively quickly, you will be expected to be a leader other sailors, even if they are not under your command in the JAG corps. As for for law stuff, you should be open to being a generalist or a specialist. Traditionally, JAGs have been jacks of all trades, but in the Navy especially there are opportunities to specialize.
In sum, I would also look inside and try to find a very good reason for why you want to join and be able to communicate that you the panel. Now more than ever there are a lot of people who are looking at JAG corps as a semi-last resort due to the economy, so you would help your chances if you can communicate to the panel that JAG is a passion more than a job.