This inability to prove beyond a shadow of a doubt whether or not something existed or occurred constitutes scientific anomalies in a nutshell. Scientific anomalies are any occurrence or thing that cannot be proven or disproved by scientific method or fact. It doesn't necessarily mean the occult, it just means something that is elusive that can be proven by circumstantial evidence or claim, but can or cannot be backed up by verifiable data. There are more scientific anomalies than one might think in a day and age dominated by scientific method and computer technology, which tends to make one believe that there is something to paranormal occurrences, whether you want to believe it or not. Where there's smoke, as Smokey the Bear says, there's fire.
Psychic phenomena make up the vast majority of scientific anomalies these days. Astral projection and astral time travel are prime examples of scientific anomalies. It is impossible to prove or disprove out of body experiences certainly, but when someone is declared dead for several minutes, then comes back to life and describes in detail what happened in the room while they were legally deceased, that tends to lead credence to the belief that some psychic phenomena has some meat to it, and if there is some truth, who can tell where it begins or ends. Unidentified flying objects and extraterrestrial beings are a very common scientific anomaly, one that many people encounter on a regular basis going back to the dawn of mankind. Explain, honestly, how cavemen drew pictures of flying saucers or how ancient Indians built calendars and artwork that is only viewable or useable from an aerial view. The Wrights didn't come up with the airplane until the early nineteen hundreds and balloons were only around for a short time before that. The fact is that psychic phenomena in most cases have some grounding and basis in reality. Psychic phenomena, while entertaining and unusual, often confuses and blurs the line between fact and probable fiction, so much so that most people don't know what to think, but in reality that is because the human brain can only take so much. Most people don't want to believe that which they cannot understand, including scientists, hence the term scientific anomaly, which is a convenient label that can cover anything technology can't explain away.