1) Pluto was actually detected in 1919, but no one noticed.
The sky, to borrow a phrase from Dave Bowman, is full of stars. Looking for something as distant and faint as Pluto is no small task. Nowadays it's a whole lot easier than it used to be -- telescopes can be programmed to scan the skies, and automated software used to look for anything that moves.
But back in the day (and I mean 1930, when Pluto was discovered by Clyde Tombaugh, or earlier) it was tougher. Telescopes had to be guided by hand. Instead of digital detectors, giant glass plates sprayed with photographic emulsion were used. They weren't very sensitive compared to modern instruments, and it would take hours to get good exposures, and even then something as faint as Pluto was near the limit of what could be seen.
A possible ninth planet had been postulated for decades; observations of Neptune in particular indicated that its orbit wasn't quite right, as if some unseen mass were pulling on it (this turned out to be wrong; see #4). In the late 19th and early 20th centuries, astronomers had scoured the skies looking for this mysterious planet, taking many photographs of the area where the purported planet was predicted to be.
The thing is, they found it. They just didn't
see it.
Once an object is discovered, astronomers observe it over time to determine its orbit. The longer you observe it, the better you understand its orbit. But once you determine that orbit, you can use mathematics to figure out not just where it will be in the future, but where it was in the past. By backtracking the orbit of Pluto once it was found,
astronomers discovered it was actually visible on some photos taken in December 1919 and January 1920 (Tombaugh's discovery images of Pluto were taken on 21, 23 and 29 of January, 1930, and he found the planet in February). Ironically, these older plates were specifically taken to look for the planet, but Pluto was somehow missed by the astronomers at the time.
It's possible Pluto was seen even earlier as well. After all,
it's known that Galileo saw Neptune years before it was "discovered"! In one of his drawings, what he labels a star is actually the seventh planet, but he didn't notice it moving. Too bad. Had he announced that, he would've been famous.