Hello new dude!
Great job! But there are a few things you need to work on.
Camera work
Invest in a tripod and/or other stabilization rig.
Tripod:
https://www.youtube.com/watch?v=xQt5-Ns-Bfw
Spider Steady:
http://www.amazon.com/Spider-Steady-Rig-DSLR-Video/dp/B005HDTKJW
Here's a good review of the Spider Steady:
https://www.youtube.com/watch?v=uBiRDXoGsCs
Don't have the money to get either of those? You could always pick up a cheap $10 - $20 tripod. It's better than nothing.
You can also turn your tripod into a stabilization rig:
https://www.youtube.com/watch?v=JW6AWmqa8ZM
If you don't have $20 to spend, practice holding your camera with more stability, or place it on a solid object like a log so that it stays still. The handheld look can look fine, but not with a smaller camera. Filmmakers that use handheld usually have a larger camera.
Also, get away from the zoom button! Yes, I know. It's tempting. It's right there, inches away from your finger. FIGHT THE URGE!
Audio
The audio isn't very good. Invest in a mic. Anything is better than the in-camera sound. At times it was hard to hear what they were saying.
Costumes and make-up
Those orange shoes looked a bit goofy
If you want to make it seem like the apocalypse, then the characters should have dirty faces and wounds. It adds realism. A little bit of fake blood and dirt, and you're good! Some slightly ripped up and dirty clothes would help as well.
https://www.youtube.com/watch?v=A-gH7f7mQoY
Also, was that supposed to be a guy in camouflage or a monster?
Properly set up your camera.
Before hitting the REC button, set your exposure, ISO, focus, white balance, audio levels, etc.
Lighting
There were some really unpleasant dark shots in the film. Get some lighting equipment. You don't need anything fancy, just go to a Home Depot (or similar store), and pick up some clamp lights.
http://www.homedepot.com/p/Commerci...-Clamp-Light-CE-300PDQ/100354511#.Uj9TQb-gUUU
And some bulbs.
Broke?
http://www.amazon.com/48690-100-Watt-Reveal-Bulbs-4-Pack/dp/B000089DC9
Always remember to properly set ISO and exposure. You may need to brighten things up in post, which can be done in pretty much any editor. What program are you using?
Story
Everything listed above is important, but the most important thing is the story.
Story > Everything Else
Some backstory would be nice. It's hard to feel for a character when you don't really care about them. Knowing their past makes the audience care for these characters, and it will be more exciting/frightening when you put them in danger because the audience has a more emotional response when they care about a character, and that character is killed and or on the verge of death. The film would also benefit from backstory about how everything came to be. Bombing? Drug gone wrong? What? But don't tell it through dialogue.
Show, don't tell.