Actually, being that this is sub panel, it isn't entirely done incorrectly. If what you are saying is what I understand, all of the equipment grounds are twisted together with the SER cable's grounding conductor. It was very common in the 60's to place them all together under one single lug that was bolted to the side of the panel. Of course, this was also before they realized that copper and aluminum don't mix well.
Now what appears to be more recently-added circuits having their EGC connected to the neutral bar is obviously handyman work. I also don't like what appears to be SEU cable used for the range circuit with the bare concentric neutral connected to the neutral bar. That cable should never have been used, although it appears to be original.
Of course the fact that what appears to be most of the branch circuit cables exiting the top through a single connector is also classic 1960's work. I wouldn't go as far to say that it is dangerous, but certainly not something that would fly these days.
I don't think that this is 1950's work because GE didn't make panels that would support the type THQP (skinny) breakers on the right until much later. I'd venture to say that this panel design is indicative of 1970's design. Of course, the panel could have been changed out at some point along the way.
What I don't understand is how the tandem skinny breakers are spaced that each half of the breaker is spanning different legs. Doesn't that mean that the cover will have a half of each slot not occupied?
I date the box mid to late 70s. 1 GE skinny breaker used, 2 branch ckt wiring copper ( al was mostly used 71-74) 3 Al feeder, during the late 70s AL was still used for feeders and big ckts due to the high cost of CU. Due to the fire problems, AL was not used much for branch ckt. 4 The large feeder looks like is has the gray fabric cover, early 80s PVC had replace fabric cover on most all cable.