Chronoscope: Not literally possible, but the combination of ubiquitous computer/sensor technology coupled with ridiculously huge amounts of computing power to assemble the evidence into a picture can do a damn good imitation of a past-viewing chronoscope. Doing the same thing with prognostication software is, alas, rather more limited, and becomes extremely unreliable more than a couple of seconds out.

(And with a powerful enough telescope, let’s not forget simply looking into/receiving signals from the past with the able assistance of light-lag.)