Note that 219mV (pd) is approx 0dBm so if this is 219mV pd (rather than emf) I'd expect to see close to 0dBm on the analyser assuming you are using a decent quality RF cable to connect to the Rigol. But your plot shows a much lower level.
In terms of initial quick and dirty checks I would check the output attenuator to see if it steps correctly right down to tiny signal levels using your Rigol spectrum analyser on a narrow span. . eg check every major step of the attenuator right down to something like -120dBm on the analyser. It should give a click or clonk each time the attenuator makes a major step change. If the attenuator is faulty you will see holes or strange level changes as you wind down the output level from 0dBm to -120dBm using the up/down key buttons in 1dB steps.
Also, make sure it gives the correct output on the two main frequency sub ranges on the block diagram in terms of frequency lock.
This probably means testing it across the range 100kHz through to 130MHz (in 10MHz steps?) and also from 130MHz up to 1000MHz in 10MHz steps to make sure it stays in lock on every step.
Also, check that every front panel button 'works' and isn't intermittent or deaf. Sometimes these can wear out although I don't know if the 8657A is prone to this or not.
Also, it probably self tests all the display segments on bootup. If so, are there any dead segments in the display?
But ideally, you would need to check it as per the manual asveedub565 states
I've never used the HP8657A as this is not one of HP's finest sig gens. The A versions have poor close in phase noise and feature quite a few spurious terms. However, as long as you don't expect to use it for semi serious testing of (for example) an HF radio or some other system that demands low spurious and phase noise then it will be fine for general use.
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