I believe this is a problem caused by chroma subsampling. In a jpeg colors are stored in a lower resolution than to brightness, this should improve jpeg compression. The human eye is less sensitive to colors, but in certain conditions the artifacts are very obvious, especially vivid colors like the red in "your" car.
When decoding a jpeg most programs will filter the lower resolution color information, to avoid blockyness. However some programs will not. PSP apparently, but also my old nokia phone, and certain DVD players etc etc.
I guess you could open your jpeg in a program that does not have this problem and save it as a png. Then open it in PSP. You should also be able to save the image as a jpeg without chroma subsampling in PSP.
Personally i never save jpeg with chroma subsampling because i know what the artifacts look like, so i notice them all the time, even when properly filtered. I guess you can join the club now  .
http://www.wfu.edu/~matthews/misc/jpg_vs_gif/JpgCompTest/JpgChromaSub.html
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