OP --
I was told last year that if an NROTC applicant wants any of the more popular Units -- e.g. Private schools in interesting areas like University of San Diego (Pacific Fleet), Tulane (New Orleans), George Washington (nation's capital), Boston U (Boston), Fordham (NYC), etc., that the application really should be in and complete by early July, well before the cutoff for the first Board.
I was told it really is first come, first served, and that these Units and other very popular Units tend to fill up, if not entirely, at least 80-90%, out of first couple of Boards (out of around 7-9 Boards, depending on year). Those first couple of Boards are reviewing files send in in May, June, early July mostly.
Once your son's applications is complete and in to NETC, I would find a live person there (last year is was P-Flying17, not sure who is there this year that posts on this Board) and ask about the then current situation at any popular schools your son has listed on the app... and change the schools and or order of school accordingly. Of course if your son wants to do ROTC at ONLY some specific schools, that's a different situation and you may just want to take the postion that he'll do NROTC at x,y,z school, but won't if it's any other school. Every applicant has their own prioroties.
One other issue -- 85% of NROTC Scholarships are mandated to go to STEM (Science, Technology, Math) majors, with a preference toward Engineering over Science and Math -- see section 2 c of this link:
http://www1.netc.navy.mil/nstc/nstc...gement Strategy for Academic Yr 2011-2012.pdf In another publication:
http://www.nrotc.navy.mil/scholarship_criteria.aspx Tier 1 is defined as Engineering, Tier II Science and Math, and Tier III other majors. Since your son in intending to major in Mechanical Engineering (Tier I), his odds are better than Tier II majors, and much, much better than Tier II.
Best of success to your son and you during this process.