Like so many others, I recently faced the issue of a broken SD card slot on my Raspberry Pi B. A thin piece of the top of the brittle SD card slot broke off, making the slot unusable since it could not press the SD card onto the contacts anymore.
I checked for solutions and found this Instructable but I couldn't find a suitable replacement SD card slot for a reasonable price, so I came up with the idea of using an Adafruit Low-profile microSD card adapter as a "slot" since I had one readily available.
Adafruit Low-profile microSD card adapter or similar (Link)
approx. 5 cm of bare wire - I used a bread board jumper wire where I took the insulation off, but contact wires from resistors or similar will do fine
some heat glue
Step 1: Step 1: Remove the Old SD Card Slot
Carefully remove the remains of the old SD card slot. First unsolder the two bigger solder connections on the outside facing side, then unsolder the other connections and clean up the solder pads. Do not use any force on the solder pads as they might chip off. I used a wire cutter to cut away the plastic that was still covering the pins from the top. This allowed me to unsolder the pins one by one.
Step 2: Step 2: Prepare the Micro SD Card Adapter
Now put some solder on all contacts of the micro SD card adapter and solder short wires to each one. The wires should stick out over the end of the adapter by approximately 5 mm - if you are in the US, switch to the metric system as the rest of the world or convert it yourself :-)
The rightmost pin pad - the power supply pin - is set back a little on the adapter. Make sure that you use a wire that is a little longer here as all solder pads on the Raspberry Pi are in one line.
Step 3: Step 3: Solder the Micro SD Adapter to the Raspberry Pi
Now secure the adapter in place on the Raspberry Pi with some hot glue. Make sure that the wires align with the solder pads on the Raspberry Pi. The lower two contacts in the picture need to stay free. They are for the card detection which is not available from the micro SD adapter. Just bridge them with some solder. Solder the wires to the Raspberry Pi and you are done!
The Raspberry Pi is now converted to micro SD.