The power supply of this spectrum analyzer is common group stabilized. Please note on the label that the minimum load on the 5V rail is 2A. If you disconnect the load from 5V, then the 12V rail will have wrong voltage.
This power supply is working correctly.
R3131 spectrum analyzer has a number of known problems with input sensitivity degradation. A correct solution to the problem was never found, but a workaround was invented. You can find information in the large thread R3131.