Indeed, those old cars did have a few serious design faults or rather were just plain outdated.

The original design was from 1924 and during the 1950s new cars were built reusing some old parts as well as parts of the design. Since the new cars had more lights I assume the circuit design of the cars in question dated from 1953 and still showed post-wartime shortages.
The pneumatic brake system was reused too, and that caused severe trouble in the last few years too, though I suppose that was mainly due to severe maintenance issues. Aside of that, compared to modern brake systems those old cars were scary anyway!
In general, the series wiring never caused problems and is still in use in older cars (up to 1976 new cars did not have inverters for the lights and several hundred of those are still in service, I guess around 250 motorcars and a similar number of trailers). All later cars had 24V DC battery operated tail lights though as well as interior emergency lights.

In the late 1960s the city decided to convert the old subway system to high platforms (95cm instead of 35), third rail instead of catenary, electronic signalling instead of light signals and the possibility of autopilot. During the transition period the old system deteriorated more and more, the electromechanic signalling system dated from 1925 after all and had only seen minor upgrades in 1965 when the system changed from mechanical tripcocks to magnets. Maintenance of the old cars was more or less cut until severe accidents required immediate action. Then cars were pretty much rebuilt, sometimes only months prior to being scrapped. The last of the legendary red 2-axle cars was in service in 1983.