I popped open my 7800 today to make sure I was remembering everything correctly, been a few years since I had one open, I had forgotten about how much a pain in the ass it is to take of the shielding...
The RCA jack on mine is part of the RF box, (physically attached, probably crimped on from the inside of the box) so it would be difficult to get to without de-soldering the entire RF module first.
If the jack is just loose, like it twists left or right or has a tiny bit of play from side to side ,AND the picture quality is still good, you could either use a high wattage soldering gun to solder the RCA jack shield back to the RF Shield... this will take a fair amount of heat to do since there is a lot of metal to heat up - Or maybe use some epoxy to glue it in place (this isn't the most ideal but if there is still a good ground contact between the RCA jack and the RF shield you should be OK. Like soldering small jumper wire to the RF shielding and then to the outside of the RCA jack for the ground connection and then glue it up....)
If the picture quality is crappy when you have the RCA cable connected and you rock the connection back and forth, then there is definitely a loose connection inside the RF module..... this is a bit more tricky to fix since you will have to perform open RF module surgery....
I would take a dremel with a cutoff wheel and carefully cut through the RF shield on the side away from cartridge holder, if you cut out a litter square it will give you access to the internal circuit board where you can solder the loose connection back together. Once you solder it up, make sure all the metal debris is vacuumed out of the RF module!! Just use some foil tape to patch up the hole you made...
Then again you can always do a composite or S-Video mod for it and bypass the whole crappy RF module all together!!