Thanks for the link, Silver.
http://www.historychannel.com/rome/"Roman coins have been dug up in America, suggesting that perhaps the Vikings or Columbus weren't the first Europeans to visit the New World. The coins were found in locations as far afield as Texas, Venezuela and Maine. One stash was found buried in a mound in Round Rock, Texas. The mound is dated to approximately 800 A.D. In the town of Heavener, Okla., a bronze tetradrachm bearing the profile of Emperor Nero was found in 1976. The coin was originally struck in Antioch, Syria, in 63 A.D."
It is true that ancient coins turn up all over, often lost by collectors, or others. It has been suggested that many fell from the pockets of US soldiers and sailors who looted them from Europe in WWII and lost them making out on the beach back home. For all of that, the fact is that MORE of these are found on the East Coast than on the West.
Ballast from English ships is responsible for some of them, also -- but not all of them.
It is also true that Roman coins circulated in some isolated parts of Spain to the late middle ages, 1500s.
For all of that, the fact is that Roman coins in America are most logically attributed to Romans.
When I was living in Albuquerque (2002-2003), a woman with a home on the Rio Grande (Rio Rancho neighborhood) brought a Roman coin to the local coin club meeting. They guys pointed her to the president. She was told that he is a high school history teacher. He told her that some farmer probably dropped it. I could not get her attention after that. I did see the coin, a mid-3rd century debased antontinionus, I think. When that coin was struck, the Rio Grande was navigatable all the up to Albuquerque and farther.
The Catheginians circumnavigated Africa.
Ancient peoples went from the Mediterranean to Britain for tin.
Ancient coins have been found in the Azores.
The real mystery is why anyone considers this a mystery.