I've recently changed my rear shock absorbers on my BMW e46 but left the springs as standard. I'm not sure if this has been a good idea. It seems very sloppy when going over speed humps and pot holes (which I always do slowly) and seems to make a bang/thump sound as well, much like if your tyre pressures are low. Can I have advice please? Should I have changed the springs as well or change the shocks back to standard (being the cheaper option)?
Which shocks did you get - they can be different grades as standard by the factory ie soft - comfort or sport - harder...
Aftermarket ones can also be different, there are even adjustable ones available.
If this behaviour is new since the shocks were changed, I would check the mount points for them. I think all E46 are the same on this, but the top mounts are inside the trunk area, the bottoms are, IIRC, on the trailing arm. Are they secured properly?
If you kept your old shocks, you could throw them back on, and see if your noise changes.
If that does not help, I would not expect replacing the springs to help you. The E46 rear suspension has a "cage" that holds the differential and upper and lower control arms. There are bushings holding that cage to the car body. That would be a suspect. There are bushings for the upper and lower control arms on each end of the arms, and bushings on the trailing arm, one on each end. Those also would be suspect.