It's pretty easy to break the SD card slot on a Raspberry Pi (I broke mine by dropping it on the SD card). If you break yours, there's no need to cry over spilled Pi. Replace the disappointing SD card slot with a new one.
Step 1: What You'll Need
Solder (Lead-free solder is harder to work with but less toxic. Choose wisely.)
Würth Elektronik 693 063 020 911
Valcon 412D02F-09PC003-SV SD Card Slot (OEM Part)
A Well Ventilated Area or a Fume Extractor
What appears to be a direct replacement for the SD card slot (Valcon 412D02F-09PC003-SV SD Card Slot) is available from Toby Electronics in the UK, but shipping to my place in Detroit is almost more than the cost of two new Raspberry Pi model B's. Currently Digikey stocks a suitable replacement (Würth Elektronik 693 063 020 911) that's much more economical for those of us in the USA.
Step 2: Remove the Offending SD Card Slot
Removing the old SD card slot is the same regardless of which replacement you choose. Use solder wick to suck the solder off of the pins and mounting tabs. Try not to put too much heat into the pads as this can cause them to separate from the PCB.
Remove and discard the old, busted, SD card slot. This is easier said than done. Anyone with some electronics experience should have no problem removing this part, but if you're new to this sort of thing, go slowly.
Once the majority of the solder has been removed with the solder wick, it should be easy to pry the old socket away from the board. Start by heating the mounting pads with the soldering iron and prying the socket away from them one at a time. Only lift the socket enough to separate the feet from the pads.
Starting on one side, gently pry up the socket… heating and de-soldering the pins as you go. Once the old socket has been removed, clean up the pads with your iron to even out any little solder messes or stray solder.
Step 3: Solder in the New Part
The OEM part should solder right in, but there's a little more to using the non-stock socket. The Würth Elektronik SD slot isn't an exact fit for the Pi. The plastic alignment pins do not line up with the holes in the circuit board. They need to be removed to allow the card slot to lay flat on the circuit board. Cut the plastic pins on the bottom flush and check the fit on the Raspberry Pi.
The pinout isn't exactly the same either. Use the flux pen to put a little flux on the pads on the PCB. This extra flux will help draw the solder in between the pins and pads. Line up the pins on the new socket with the pads on the board starting at the left side in the picture above. Solder a couple pins to hold the SD card in place. Finish soldering all the pins and the mounting tabs near the edge of the PCB.
The two card detect pins (on the right in the picture above) need to be bridged as they are not present on the new slot. A little extra solder does the trick.
For more detail: How to Repair a Broken Raspberry Pi SD Card Slot