Some ideas to explain some anachronisms:
Tubes vs Transistors : I believe that Fallout world tech was actually very similar to what we have today but as the fear of nuclear war grew in the world, science began re-investing in vacuum tube based technologies. I believe its likely that this interest in tube research began somewhere in the 2020's. Improvements in this design mean that by the 2030's-2040's it was sufficiently advanced enough to be used in robotics (Mr Handy) and by the 2050's-2060's were advanced enough for AI and large-scale systems (ZAX). By the time of the great war tubes could be miniaturized and were efficient to a level that they could be used in Pipboys and other smaller computer devices.
Non-color TV: I believe the general economic depression caused by the resource wars combined with the switch to a new tube technology caused most newer tv's being made to be B&W, the downside being obvious but the benefit being such displays had a longer life. Similar explanation for chrome type computer screens.
Lack of advanced PC Software / UI : I think what examples we have seen of computer games (Grognak!) in the Fallout world are the way they are because the technology was still new to the home and general civilian programming of such devices was reaching a point similar to 1983-1986 in IBC PC programming/software. Clearly military and industrial users had more advanced software, though still limited UI's (text based). The UI limitation may be caused by a limitation in graphics displays.
Culture : The 1950's style culture may just be an adoption of the same for nostalgia purposes. People in this point in time are paranoid and maybe have adopted this culture for the 'simpler', 'safer' time period it represents compared to their own time. This would be why oldies music is prevalent.
Holotape : These are impressive storage devices. Obviously EMP proof and designed for very long lives. That they (only) store 4TB by 2077 says that this was again a new tech that was designed from the ground up to be nuke proof, and probably still relatively new to the time period.