Most people's biggest mistake after filling out a Walmart application is they merely sit at home waiting for the call that sometimes, unfortunately never comes. You can wait but it shouldn't come as a surprise that most companies, especially in today's economy, because of the large volume of applicants, can't respond to each and every application. The same goes with WM!
So, it should become your job to follow up after your application within the first 2 weeks either by phoning them or visiting them in person. Personally, if I'm going to take the time to fill out and submit an application anywhere to any company, the first thing I would do is make a plan so I can have as many job opportunities as possible.
I would list 4-5 companies at a time to work for and submit applications to, say only 2 the first week, and 3 the following week. This would give me 5 chances to get hired. Of course, a Walmart job would be at the top of my list followed by, maybe Sears and Target!
It really makes no sense to take the time to prepare yourself to get a job by looking for and researching for hours on end for a Walmart and other jobs, then not taking the time to simply follow up consistently on each and every application submitted. If you don't check to see where you stand, why even bother submitting an app in the first place?
Imagine someone submitting 10 applications for different companies and getting a call back from only three of those after a couple of weeks; this is today's reality. You can drastically tilt that figure in your favor and get a response from almost all of them, by making your intentions of wanting to know the status of our application consistently known.
When visiting the store you're hoping to get hired at, take the time to dress yourself in comfortable, crisp clothing and try to make a great first impression. Many successful applicants actually visit the store of their choice prior to filling out an online Walmart application so they can make contact with the manager or other hiring personnel. This, without a doubt, can give you an advantage because humans love hiring other humans who are familiar to them, and if you make a good first impression, you'll already have an advantage.