Question: I would find it more interesting/organized if there was a theme to follow for the featured images each week. For example, this week post only pictures of cars, flowers, landscape or whatever and change the theme every week.

Answer: 
I think this is a good idea too. I think @Jay brings up a good point about managing the which weeks have themes and what the themes are. I figure interested parties can hash out a system if we do choose to go with themes. 

Here are a few random ideas (one stolen from @seanmc):

* Unedited (strait from the camera, make it as perfect as you can with nothing but physical equipment)
* Photomanipulated (do something unconventional, add photographic elements and blend together a new reality...or surreality, or something completely unreal!)
* Brilliant Sunsets
* Monstrous Mountains
* Micro Macros
* Pure Portraiture
* Dripples (closeup water shots...ripples, drips, droplets, etc.)
* Birds of a Feather (any shot of birds)
* Wild Life (wildlife..duh!)
* City Life
* Nuanced Night (any shot from nighttime)
* Astrophotography

As an added thought, from a management perspective, it might be good to have a "Theme Announcement" thread a week ahead of time to give people time to go out and get a shot for the upcoming theme (if the next week IS a theme...to @dpollitt's point it might be best not to have every single week be a theme week.)
The contest idea, this is similar to many photo sites I am familiar with in the past. 

Personally I don't typically have time to go out and shoot the theme every week, so I would likely participate less if ever.

It does have some merit to expand your portfolio or challenge one, but it's just not my favorite way to shoot or think about shooting.