Those early spec ans have pretty bad front ends. Not sure about that one, but some (like the Tek 491) have shitloads of birdies and it's almost impossible to determine what's real and what's not.
It just requires a little more "user input" to separate the real signals from the spurs

I used an old pair of Tek "1 Series" plug-ins for several years (1L10 and 1L20) and you differentiated the actual signals versus spurs by the direction and rate at which they moved across the screen when the center frequency was changed. I picked up a Tek 7L13 a few years ago which is much easier to use. The analyzers sure make it easy to align the old phasing rigs.
Pretty much any spectrum analyzer is better than no analyzer; modern analyzers definitely are easier and don't require as much skill to use (a slightly trained monkey will suffice for the current offerings). Enjoy your new trade.
Rodger