Avoid stutter when watching Amazon Prime video on Mac Mini 32-bit?
My guess is that your CPU just isn't up to the task of decoding the stream of data that makes up the video stream for several reasons.


Amazon video is using a somewhat inefficient codec and software stack to deliver the content.
The software to render the video is likely single threaded on your Mac OS.
Your CPU has only two cores and at 1.66 GHz of that era isn't keeping up.
Your desktop size is too large and/or you can't ask the video server to send a smaller picture that can be processed. Each time you double the sides of a rectangle, you have to calculate 4x the pixels. Even reducing from 1080 horizontal pixels to 720 horizontal pixels would drastically reduce the processing power needed to render the video.


You can verify that the CPU is indeed the culprit by rebooting your Mac and opening only the Activity Monitor app and watching the CPU graph. Set the update interval to be 5 seconds in the app and then open your web browser of choice to an empty page. Again, let the CPU settle. Lastly, load the video you want and then pause the stream.

Looking at the CPU load at that point will let you know if any other process is hitting the CPU in a meaningful way. Anything over 5% would be worrisome from a maximum performance standpoint.

Then let the video play and watch the CPU allocation. 

Knowing that the CPU is the problem, you can try reducing the screen resolution or putting the browser on an external display VGA or reducing the color depth of the main display might all help or hurt CPU load - so running some controlled tests might get you to acceptable settings. If not, you could get a secondhand iPod touch or iPhone/iPad and probably stream Amazon video inexpensively and far more smoothly than your Mac.