Just opened my Retro Freak the other day and started loading games onto it. Like OP says, the SNES slot grabs tight, but wiggles quite a bit, and after the first few times a cartridge was inserted I've had a lot of trouble getting cartridges to be consistently read ever since.
My strategy has been to insert a cartridge, refrain from moving my hand, and press down on it after insertion long enough to get the Retro Freak to read the cartridge and dump the rom. From there, I try to ... "slowly" ... take my hand off the cartridge, but it sometimes still gives up the ghost and says "Oh there's a problem reading the cartridge please try again!", so its pretty frustrating.
I see where the cartridge reader is attached to the device with screws. I wonder if replacing it entirely with a new/different reader would fix the issue. Then again, I'm not eager to try that with my "own" Retro Freak. I just got the thing. Heh.