For my shop, your vision has to be correctable to 20/20 and for guys that are really nearsighted, you have to be able to wear soft contacts. They're ok with Lasik or PRK too. So check on that with your local agencies.
As for whether you want the job or not, it's dependent on an individual. You being a military vet may serve you well, because it's less likely to be a decision based on boredom in your current job. I wanted to be police for several reasons, and none of them were the idiological BS that you hear people talk about. The job provides me with personal satisfaction that can't be taken away by media slander or prevailing political winds. I like the paycheck and the relative freedom this job provides also. Guys that think they will make a difference and be recognized for their selfless sacrifices are in for a dissapointment.
ETA: the "AHA" moment wasn't there. It was a culmination of things. I worked in an office, punching a keyboards and felt that I didn't work with people enough. I witnessed a couple of occasions when cops did some truly heroic things. Then 9/11 happened and it pushed me over the line and I finally figured that this was what I was going to do. Then I worked for a PD as a civilian for a bit and got a lot of encouragement from officers there, which helped solidify my decision. I don't regret it one bit.