Let's discuss a bit more of your one post ...
"I do like the long zoom but at either extreme it is no good. Zoomed all the way in gives about a 120 degree fish eye effect and zoomed all the way out the image quality is pretty much unusable. This shot is all the way in."
Spend a bit of time investigating focal length's effect on your photos. It is not simply a matter of getting closer to a subject. Begin with focal length and perspective;
Nikon | Imaging Products | DSLR Camera Basics | Perspective
"I had it on aperture priority with the lowest setting it would allow but that is as much depth of field as it would do. When I first saw the shot I thought it focused on the tree behind and to their left but I had it center weighted so it shouldn't have."
OK, here's your real world limitation to the tiny sensor of the bridge camera along with its greatest strength. A larger sensor will almost always be more light sensitive when you have a wide open lens which, had you used a DSLR with a "fast" prime lens, would have allowed a lower f-stop for that shot.
Of course, if you say you want the APS-C sensor, then you must begin to look at DSLR's in most cases or move to one of the "enthusiast" level bridge cameras. With the DSLR you have to consider just which lens you might have used for that shot. If you were using a zoom lens, then you have a lens that doesn't normally start off at a low f-stop value. Zoom in and, unless you are using a lens with a constant aperture, you will be raising the aperture value (stepping down the aperture) as you increase the zoom. This is going to be how most moderately priced zooms operate. The result is you are not assured a zoom lens on a DSLR is going to provide the type of background blur you feel would have improved that specific shot. A faster prime lens like the 50 mm f 1.8 I mentioned would have but you would have also needed to place yourself within a comfortable shooting distance for that focal length.
There will almost always be a trade off in this hobby.
As you can see though, as objects at a further distance from the lens begin to blur progressively more and more, this is how you must begin to think about your shot if the result you have in mind is making the foreground subject(s) pop. That's the clue to take away from Britton's shots mentioned in my first post. It's the set up of the shot that works to get you where you envision being.
And, at times, you simply must live with the limitations of your gear. No matter what you own.
Now, just as the small sensor of the Panasonic provides the zoom power of the lens the size of the sensor also effectively ups the real world aperture value of the lens. I'm sure one of the more technically oriented posters can give you exact numbers but the basic idea is, the smaller the sensor the smaller the relative aperture for any number designation. Think of that as saying a f-2.8 lens on your bridge camera is not the same as a f-2.8 lens on a APS-C sensor.
What is the equivallent aperture on different cameras with different sensor size?: Open Talk Forum: Digital Photography Review
So, while it's true you would have likely had more background blur if you had taken that shot with a DSLR and its lens, you also have to consider just what you had to do to take that shot with the DSLR. If you had a long distance between you and the main subjects and you had used the zoom power of the small sensor/lens combination, that's probably an advantage over a DSLR with less reach to its zoom lens. If the DSLR/zoom combination raised its aperture value to reach that shot, then it's quite possible the result wouldn't have been that different than what you have now.
You might also consider how you would otherwise achieve that shot with a different camera/lens that sported higher "resolution". If we simply restrict the idea of resolution to the number of megapixels you have available, you might end up cropping the DSLR's shot to achieve a similar apparent focal length. Once you begin to crop, you will begin to toss away megapixels. If you begin with twice as many, then it's unlikely you will reduce your image to an equivalent number but this is a shot by shot situation. Therefore, "resolution" is another value which will not remain constant simply because you've paid for a more expensive DSLR.
What is the equivallent aperture on different cameras with different sensor size?: Open Talk Forum: Digital Photography Review
Re: 24 Megapixels vs. 16 vs. 10 - How much of a cropping advantage?: Beginners Questions Forum: Digital Photography Review
And, of course, if your print out your own photos, the resolution of your printer will affect the total resolution of your final product.
More on "resolution" later ...
I assume when you say the camera was set to "center weighted" you are referring to your focus point(s). Not how the camera metered the scene. I'll certainly accept any correction from anyone more familiar with the Panasonic system, however, "center weighted" on my Canons refers to metering while focus points and the size of the focus frame are set in the menus. Focus (on my Canons) is not referred to as "center weighted".
"It is a bit concerning that my shots would be no better with an SLR. I was thinking there would be more resolution and saturation and just over all better image quality with an SLR."
Other than your shot of the couple (where they are in shade) there is more than sufficient light available for any decent camera to operate at close to its best performance. Given enough light, even the most modest digital camera can provide good to exceptional results today.
15 Stunning Photos You Wouldn't Believe Were Taken With A Smartphone
This site restricts its users to photos taken with less than a DSLR;
Emphoka
It really is the photographer understanding their equipment and the basic rules of photography that makes your shots;
Photographs taken on and edited on an Samsung GALAXY Nexus | Photography Forum
If you are shooting in RAW capture, the "resolution" of your camera is fairly well fixed depending upon your setting for aspect ratio. You will have access to the data as it is taken from the sensor when shooting in RAW capture and thus the greatest amount of control over your final result.
If you are shooting in Jpeg, you have control over many of the in camera adjustments made to the photo as it appears on your camera's LCD or on your computer monitor. You can increase or decrease the "resolution" by setting the camera to a larger or smaller file size. Use your owner's manual or a forum to determine whether your Panasonic can be set to the equivalent to "SuperFine" resolution if you want the largest file size from your Jpegs. Otherwise, simply set the camera to the highest file size.
Color saturation can also be controlled by the user when shooting in Jpeg capture. This is probably located in your menus and can probably be set to a custom color setting (or two).
Also, don't ignore the effects of various white balance selections when shooting in Jpeg;
How to Set White Balance
You can correct white balance in post production if you are shooting in RAW capture.
Next, realize the time of day and the season will play a part in the saturation of colors;
How to Get Great Colors
If you have not yet sat down with your camera and your camera's owner's manual, do so and make the adjustments necessary for the photography you wish to take.
Understand you have considerable control over how your photos turn out and you needn't - and shouldn't - just accept the factory defaults from the manufacturer.
Hope that helps.