Granny,
Most of these ooparts I've investigated to some degree or the other.
For most of the rest of them there is nothing but the written word to investigate.
But as an overview:
The Coso artifact actually
is a spark plug from the twenties which became enclosed (encrusted) by what's called a "concretion." Not unusual at all, such formations form in a very very short time (thus the "concretion" name.) It's sometimes said it was found in a geode, but nothing could be further from the truth.
The Ica stones were exposed as fraudulent (the oopart ones w/dinosaurs, anyway) on the BBC program Horizons, several years ago.
The Acambaro figures have not been dated. Claims have been made, but none shown to be true for their dates. These figurines are privately owned and the current owner refuses to allow them to be analysed.
All but one of the so-called crystal skulls have been shown to be of modern (1800's) origin due to the polishing patterns found on their surfaces. The single exception, though beautiful and amazing, could have been carved out in a time span of a couple of years by natives in S. America, though a craftsman would certainly have to be dedicated to do it in that time frame.
The Dropa (or Dzopa) Stones are an admitted hoax.
The Baghdad Battery and the Antikythera mechanism are real objects discovered (or verified) by archaeologists. The actual use of the battery is unknown, which means that although it could have been a battery, it could also not have been. It's output wouldn't have been enough to accomplish much beyond something like electroplating, though, and even that would require days at the voltage available. On the other hand, in an age that knew nothing of electroplating, imagine how easy it would have been for some dishonest person to plate gold on some heavy metal and pass it off as pure and you can see that it's just not exactly beyond all comprehension that it was used for this very purpose. Such a use could have been easily discovered by accident however. Have a look at "wet cell corrosion" to see how this might have happened. One need only to observe the slow motion reaction between dissimilar metals that are in contact and wet, like iron and copper laying out on the porch in the rain together, to be in a position to "discover" a battery.
The Antikythera mechanism is an exciting object about which very little is known and much is speculated. There is no doubt that it's gear mechanisms are more complex than were originally imagined for the Greeks, but it post-dates Archimedes and several other Greek geniuses, as well as many fairly astonishing but well known Greek inventions, so it's just not completely "out of place."
The "grooved spheres" are a naturally formed deposit that has occurred in other areas. Only a single one of these sphere has these grooves which most likely did
not form naturally but were scratched into the surface after the sphere was unearthed. The "metallic" makeup is not nearly what it is claimed as to hardness, the mineral it is made of varies in hardness greatly. IOW, perfectly natural.
Almost all the "things found in coal" or whatnot have been either
shown to be or
admitted to be hoaxes. If you notice, almost every claim comes from the 19th century, a time when such things were being constantly written about or hoaxed/joked about (Paul Bunyan, Calaveras County jumping frogs, etc.) Anyone want to speculate why no such objects are found today, even though roughly a hundred times as much coal mining occurs in the present than did back then?
I'm not going to the second page of the link I went to. If you want to, you can ask me specifically about whichever ooparts you are particularly interested in and I'll post my answer here.
Suffioce it to say that these "ooparts" are, in the majority, not mysterious in any way and are absolutely not out of place at all, except in the minds of the "true believers."
Harte
Or maybe it was the British? 
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