Chris is correct. The memory map allows a total of 31K continuous memory, of which at least 0.5K somewhere preferrably is screen memory. There is another 8K RAM/ROM slot, and a few I/O blocks that are unconnected. In theory you could fill the latter with RAM or ROM, but it would make a very non-standard VIC-20.
Cartridges seldom go loose once they are inserted, much because they are wider than they are tall. Memory expansions for ZX81 were dreaded to fall out, but I think it was due to their physical appearance. Actually, I think a C64 cartridge will be more unsteady than a VIC-20 one.
As I wrote earlier in this thread, if you're going to install something internally in your VIC, I suggest the expansion board before piggy-backing RAM chips (if you can find them - the first revision VIC uses 0.5K chips and the CR revision uses 2K chips IIRC).