Space Shuttle 10231 Stability on base
According to Brickset there were indeed stability problems with set #10213, which was originally intended to be a strictly display piece for the 16+ age group.
As a response, the 10213 was retired, and a reinforced version (#10231) has been sold instead. If you are stuck with the first, unstable edition, you could try applying these alternative instructions.
You'll need these parts:

According to Brickset commenter Enosh_Kasra this service pack can be acquired through LEGO customer service (at least it could be in 2011).
And this is the disassembly and reassembly instruction sheet:







This seems to strengthen the External Tank and its connection to the Shuttle, and does not address the four points of stability you mentioned, but I might be wrong. And the extra strength will definitely reduce the number of sub-assemblies after an Unplanned Rapid Disassembly event.