Assuming we could overcome the technological/scientific/physical limitations and we did have a 'realtime' video feed from a Google Earth-like perspective of events happening 65 years ago (picking the final example)... I wonder what the societal impacts of that would be?
For one thing we might be able to measure the polar ice caps -- I don't know how far back our current data go, but I don't think they go back to 1950. Maybe spectronomy (?) could tell us something about the proportion of greenhouse gases.
If the telescopes had adequate resolution, we might be able to measure the size of cities over time. Images from 1950 forward might give us data on the progress of city growth and electrification by observing the spread of night-time illumination.
It's fantastic to imagine similar data going back centuries or millenia. It would be remarkable to chart the growth of Rome, London, Delhi, Beijing over time, or perhaps gather demographic data on the spread of the "barbarians". Or track the agricultural and demographic history of Egypt by watching the spread of cultivated land around the Nile delta. Or gather data on the history of trade routes like the Silk Road by observing the growth of towns along them. We might track the history of the Black Plague by observing the shrinkage of cultivated land, and the pause in the growth of urban centers.
We might learn a lot of climate science by gathering data on the explosion of Krakatoa and the subsequent effects on the polar ice caps.
We might gather data on the emergence and spread of agriculture from pre-history by observing transformation of forest land into farmland, and the appearance of greenery in places supportable only by irrigation. You might tell the story of the Tigris and the Euphrates that way.
Of course, all of that depends on spectacular levels of resolution. And those would have to grow as we looked back further in time, because the lensed light would appear that much further away. I suppose most of what I've listed here could easily be outside any plausible resolution. I guess I imagine that some of climate science stuff might be dreamt of.
Using the GP's figure of 65 years ago, you could check out Elron's claims. Scientology was founded in 1952. Dianetics was going crazy for a few years before that.
Other than that we need to find some MACHOs between ~700 and ~1800 lightyears away in order to check the claims of the more popular religions.
But, considering the data would be coming from the scientific (and in particular the atrophysics) community, it would be ignored by those who found it inconvenient.
Religion and Astronomy have a very checkered past.
