Considering the history of astronomy, we see that several phenomena known today were within observational reach much earlier than when they were actually discovered. Heinrich Schwabe discovered the solar cycle in the 1840s, after almost two decades of diligent telescopic observations. Numerous records of sunspots visible to the naked eye are preserved from ancient cultures, though, and it is known (see e.g. Schaefer 1991) that the number of sunspots visible to the naked eye follows the same 11 yr cycle as the relative sunspot number (found via observations with telescopes). Using suitable eye protection or taking advantage of when e.g. thick clouds dampen the sunlight sufficiently, an observer in ancient times with enough stamina could (as others have pointed out) have discovered the solar cycle.
However, just because a phenomenon is within technological reach to observe does not mean that there is sufficient awareness or interest to even ask the questions leading up to its discovery. The Sun had already been under scrutiny with telescopes for over 200 years when Schwabe made his discovery, and there is slight reason to believe that ancient solar observers would have been able to pose questions leading to a prolonged observing campaign revealing the solar activity cycle. Today, the scant ancient observations of naked eye sunspots are being collected (see e.g. Wittmann & Xu 1987) for use in modern solar studies.
What else could be hiding in ancient astronomical records? Studies of transient celestial phenomena such as comets, meteor showers and supernova explosions have used pre-telescopic observations to gain valuable insights. As astronomy develops, new questions are raised, and even gamma-ray bursts (GRBs) have been addressed from the perspective of historical records. These short (seconds to hours), extremely luminous bursts of gamma rays happen anywhere in the sky and are found at a rate of about one per day. GRBs usually occur at distances of billions of light years and likely arise from either certain types of supernovae or from merging neutron stars. Their optical afterglow is usually invisible to the naked eye, with at least one clear exception. The GRB 080319B, observed on 2008 March 19, reached peak visual magnitude 5.3 and was within naked eye visibility for about 30 sec (Racusin et al. 2008).
This GRB inspired Strom, Zhao & Zhang (2012) to see if any historical record of other naked-eye GRBs could be found, also asking what any such historical record could tell us. Using statistics of optical counterparts of GRBs from 1997-2010, they demonstrate that at least 10 GRBs of about the same magnitude as GRB 080319B happen per century, and that 2 GRBs per century should reach magnitude 3 (a brightness comparable to the faintest star in the Big Dipper). A handful of times per millennium, they estimate, a magnitude 0 GRB (bright as Vega) could appear in the sky. While unlikely, a naked-eye observer with good knowledge of the night sky could notice a visual GRB during the seconds or minutes it is visible. Vetting old Chinese records, Strom, Zhao & Zhang found a handful of candidate events, an interesting one coming from 1855 August 16 (of a “star of red color” visible “in the southeast” for “about 7 minutes”). The vagueness of the record prevents further follow-up, though. Discussing the use of a possible recovery of a naked-eye GRB from historical records, Strom, Zhao & Zhang argues that a study of the GRB remnant after several centuries could maybe benefit. Even without a GRB remnant identification, they point at how identification of a historical naked-eye GRB could help constrain the rates of such rare events.
With the above examples from investigations inspired by observations made with the naked eye throughout history, it is staggering to think about what can be learned from renewed investigations of such a rich material as the photographic plates taken at observatories around the globe during the past century and a half. While our knowledge will never be complete, we nevertheless have the ability today to address astrophysical questions undreamt-of when the plates were taken decades ago. Extreme phenomena and beautiful patterns of nature likely hide within plain sight in photographic plates and other records from the recent past of astronomy. The VASCO (Vanishing & Appearing Sources during a Century of Observations) project intends to explore this.