What advice do you have for a Marine who is trying to get a job with local police?

A great deal depends on whether he is trying to get in with municipal, metro or county. Sounds like "local" equates to municipal. When I left AD, I went through the process of getting an offer from my local city police, was given the offer, and ultimately, received a better offer I took instead. Here's my experience:

First, I started looking for hiring departments close to where I wanted to live before I left AD. I contacted people at those departments to get a read on what their process was, and what they were looking for. Some city police forces have "revolving doors"...i.e. most guys go in for a year or two to get their certs, then apply to Metro or State. Others, are the "goal hire" for people coming up through county Corrections...but that's normally for the Sheriff's Department (generally speaking, one doesn't become a deputy without a political connection to the department). In my state, having a certification meant you could directly apply, and you could pay for the academy on your own, as part of a scholarship for a CJ degree program, or as a condition of being offered a spot on a local force. I wasn't looking to spend the money, so I went the last route.

I targeted a medium sized force that was looking for permanent, long term minded applicants...it helped that I had formed a connection with the Captain who was in charge of selection. It was small enough I could advance, but large enough that I could get a decent salary. Their deal was that if accepted, they covered the cost of the academy, and paid you while you attended.

They only had three spots, and about a hundred applicants...the initial screenings necked that down a bit, and after a physical, PT exam, practical test, and interviews, I had the offer. Candidates that made the cut, but came in fourth and down, were offered alternate spots-that means the number 4 guy got my offer when I went the other way.

From what I could ascertain, the academy isn't really a "joke"...but for anyone with military experience and in reasonably good shape, I'd say its just getting it over with. Unless of course, you're applying to a major metro department like NYPD...I understand those programs can be pretty daunting. Again, no sweat for a Marine. I started training for it about three months before applying, and figure that if I had gone...I'd have been alright, even at the "ripe" age of 30.

Ultimately, I chose not to become a cop because on top of family pressure not to, I needed, and was offered better pay sitting behind a desk.

If you have the means (sufficient employment) then apply, take proper courses, and become a Reserve Officer in the agency you desire. You get to start doing the job, the Agency gets to teach you, and the Agency gets to evaluate you as a full timer. If money is an issue then apply for non-sworn jobs (dispatcher, parking, animal control, custody). You can turn that into an opportunity for a sworn position very quickly.
Breaking into LE is harder than it should be at times. It's very picky yet takes folk that never should be in it. That can frustrate. Nepotism is huge in every agency also. Most agencies have a ready pool of Reserves to choose from too. Furthermore, agencies are required to test and have an active list of prospects each year. In case a bunch of us quit or die en mass Personel is ready to get new bodies. That being said, it does not mean they hire from those tests every year. So find a way to Adapt and Overcome as Clint says. Go Reserve or non-sworn first. Those "issues" may not be as important at the Reserve/Non sworn level. If the agency passes you for a lesser level they will likely pass you later on.

Not sure why but, my first thought was forget he is a Marine while applying for the job.

Yes, I know, a Marine never stops being a Marine. But, sometimes being a Marine can scare others in the civilian world.