The list of career mode general achievement contracts

Currently (0.23), there is few practical difference between sandbox and career mode after you unlocked the whole tech tree. You have all parts available and are free to use them to do whatever you like.

The only difference is that you can still use experiments in career mode, while in sandbox mode all experiments are disabled. This doesn't give you any gameplay benefit, but it gives you the opportunity to read the flavor texts of the experiments performed on outer planets and moons. Some of them are quite interesting and/or entertaining. One EVA report on Eeloo is really cute, by the way.

Currently there is a lot more science to farm in the KSP solar system than you need to unlock the whole tech tree. And considering that it is planned that more planets than just Kerbin, Mun and Minmus will gain different biomes, the science output will just increase. If and how the developers will balance this in future updates (more tech tiers? Make later tiers more expensive? Scale down scientific values? New uses for science points?) is currently just guessing.

Since version 0.23, the Mystery Goo Containment Unit and the SC-9001 Science Jr. can not be reused after you transmit their science data, unless you have a Mobile Processing Lab on the vessel (or dock with one which has). The MPL can "clean out" these experiments so they can be used again (It can also "process" any science data so you receive more science through transmitting them). You find these option when you right-click the MPL. Note that both of them require a lot of electricity, so your space laboratory should be equipped generously with batteries and solar panels.

Update: In current versions (since 1.0?) astronauts of the Scientist class can also reset these experiments while on EVA. To do so move the Astronaut very close to the part, right-click on it and pick the appropriate option.