I retired from the US Army (22 years- 16 active, 6 reserve) and I've been a police officer for almost 10 years. My agency is a progressive, community oriented municipal department. if you don't think service in the armed forces is beneficial, you haven't widened out your thought process. Here are just a few examples:
1) problem solving (bread and butter for law enforcement officers)- In the military service, you have to think creatively to get missions accomplished. You have to be flexible, an independent thinker, but be able to work in a team setting to get results on a time sensititve basis.
2) dependability - As a Soldier, Airman, etc, you're supposed to be at your appointed place of duty on time, in the right uniform and ready to do your job. You're expected to do your job, even if nobody is standing right over your shoulder. Integrity, honor and loyalty mean something in the military.
3) cultural awareness/diversity - In the service, you work with people from all over the country, and around the world. You learn to relate to people from all racial backgrounds, socioeconomic groups, and different political viewpoints. You learn from day 1 that the color of your skin isn't important, but how you do your job.
These are just a very few isolated examples. If you look on almost any job posting for a police officer, I bet you'll find words very similar to what I've written above. I could go on and on. I was an FTO for several years and there was a distinct difference between veterans and people with no military background. Veterans in general know how to take *** chewings (in cop talk, "Daily Observation Reports") They are more adaptive thinkers and generally more mature than other people their age who come from the civilian work force. If you think, "All I do is hump a rucksack and go to the field," open up your perspective.
I was a cavalry scout before I went into law enforcement. Since I began in my current career, I'n become a firearms instructor, rifle armorer and ops support officer, all based on my military experience. Here's a picture of me at the range in May, having more fun than one guy should be allowed to.