Awful background image quality in Android

First of all, make sure that your original image looks good so you're not just getting the problem from there.
Then, in your onCreate() method, do:

code1:

getWindow().getDecorView().getBackground().setDither(true);
getWindow().setFormat(PixelFormat.RGBA_8888);

Deprecated:

getWindow().addFlags(WindowManager.LayoutParams.FLAG_DITHER);

And to load your image explicitly as a 32-bit image (RGBA-8888 configuration) add the following where you load your views:

code2:

BitmapFactory.Options options = new BitmapFactory.Options();
options.inPreferredConfig = Bitmap.Config.ARGB_8888;
Bitmap gradient = BitmapFactory.decodeResource(getResources(), R.drawable.gradient, options);

findViewById(R.id.main).setBackgroundDrawable(new BitmapDrawable(gradient));

Comparison between different approaches: (these are all screenshots from the resulting application)

My source images (64 colors to the left, 24 bit to the right):
image1 and image2:

1: Raw 64-color image (image1) set as background from layout XML:

2: The same image (image1), using code1:

3: The same image (image1) using both code1 and code2:

4: image2, loaded with code1 and code2 (in this case the dithering is not really important as both the source and destination use 8 bits per color):

Notice how the resulting artifacts in image 3 already exists in the original image.

Note: if anyone knows how to shrink the images down a bit, feel free to edit this post...

The problem is your PNG has been converted to 256 colours, open your APK in your ZIP tool of choice and check manually. If that's the case, make sure that your PNG has:

1. An alpha channel
2. One pixel which is slightly transparent

This should prevent it from being converted to an indexed palette.