I picked up a slim that was stuck in an install loop for dirt cheap. At around 39% I got error code 8002F1F0 when installing the latest firmware. I did some interweb searching and found its more than likely the bt/wireless module causing issues. All the users with the fat consoles fixed the problem by a simple part replacement. The slims aren't so lucky. Someone mention a reflow or reball of the module. I have the equipment for the reball so I went ahead removed the module, placed some .76mm lead balls on by hand and put it back on. To my surprise it worked. Which leads me to ask how could this even break a solder ball/connection? Its just a basic bt/wireless module. It can't be getting that hot and I would think board assembly at the factory should be on point... The console still had its warranty sticker so it had never been opened.
If you study the design of the PS3 slim you will see it's extremely vulnerable to upwards punching or mechanical shocks on the bottom of the casing. It's possible that the unit you repaired had cracked joints under the BT/WiFi module due to mechanical stress. (perhaps the original owner let it drop ?) This 8002F1F0 means the updater was unable to complete the update step where it uploads the updated flash image to the bluetooth hardware. WiFi firmware is loaded into RAM on the module during the console boot so it can't screw that part during a update.