"It depends"
For constructing spheres and things, you could always fabricate two (or more) parts separately, and then stick them together at the end, though this isn't ideal.
The rough edges is more an artefact of an 'unpolished' toolchain. If your design program exports models with large facets on curved surfaces, the product is going to share those facets even if your CAM and driver software/firmware is perfect.
Poor rendering of curves or non-axis-aligned straight lines is at least partially a software problem. In theory, a reprap should be able to make very high quality smooth curves *in the XY plane*. Better driver software and hardware will make this a reality... this isn't an unsolvable problem. Having smooth vertical curves is much trickier, due to the way that objects must be layered and printed; this may be far harder to resolve and maybe even impossible.
Lastly, it may always be possible to increase the resolution of the fabricator, with a finer filament and smaller XYZ steps. This presents many more problems however, requiring a much higher precision cartesian robot, and inevitably lengthened build times.
Quite often however, these things should not matter too much.
Considering syringes... you could have a square section one, perhaps
Also remember than in syringes the important bit is going to be a silicone gasket to form a seal betweem the barrel and plunger, and given its squishy nature a less than perfect barrel isn't necessarily going to leak.
As for interlocking components, that I'm less sure of. But recent output from nophead's machine is impressively high quality.
Lastly, we only have the one toolhead right now. Support material extruder will vastly extend the range of things a reprap can make. And there's nothing to stop you sticking a milling head on too, given a strong enough frame. Given time, all things will be possible