Inter-Continental Travel possible pre-Colombus?

The idea wasn't exactly laughed at, or else archeological digs would not have been done. The Norse (Vikings) were also in a good position to reach America compared to other people, since they took a route which allowed them to hop through the North Atlantic which made for much shorter trips. As well, they had proven techonology for ocean-going boats, something which most other civilizations didn't.
 

To my knowledge, these finds are hoaxes. Think about it: why would a Roman helmet turn up in Tucson, out of all places? I mean, had it been Virginia or somewhere in the Carribean, it would have made more sense, but Tucson?
 

Read the following article on this. The presence of nicotine can be explained by two factors: 1. There are otherr plants than tobacco which contain nicotine. 2. The 19th and early 20th century archeologists who discovered these mummies smoked a lot around them: the smoke impregnated the linens in which the mummies were wrapped.

http://www.hallofmaat.com/modules.php?name=Articles&file=article&sid=45
 

Remember that some of these items (Roman armor, old world coins, etc) could have easily come to the Americas in more modern times, and either lost and rediscovered or simply planted in order to obtain publicity. Most of these "sensational" discoveries have already been exposed as hoaxes, yet they continue to be cited as proof by various pseudo-scientists and new age writers. Take this type of evidence with a grain of salt.

As for boats, it is one thing to build a boat that can travel short distances in sight of land and something else altogether to build an ocean-capable vessel which can withstand a voyage of several weeks in potentially rough conditions. And then there's the whole issue of navigation (it's darn easy to get lost) and of motivation (how do you know that there may be something out there and you are not embarking on a hopeless voyage?

All this being said, absence of evidence is not evidence of absence. There may be more discoveries made which could prove beyond doubt that other people were trans-oceanic voyagers. But we simply can't prove that based on the evidence available today. If we could, the scientific community would accept it, as they did with the Vikings visiting America.

As for the Vikings picking Newfoundland: just look on a map: it was the nearest inhabitable land area accessible by boat for someone coming from Greenland, as the Vikings were. Tucson on the other hand, is 1000 km inland from the Gulf of Mexico and more than 2000 Km away from the Atlantic seaboard. How did it get there? If the Romans had left it, it means that they went that far inland, which implies a familiarity with the coast, in which case we'd expect some Roman artifacts to turn up on the coast somewhere. And there's no such thing. There's also the possibility that these roman artifacts got there through a native trade network. But then again, why don't we have evidence of any other artifacts anywhere else? Finally no Roman documents ever mention a voyage to America, and Roman ship-building technology was actually very inadequate for a Trans-Atlantic voyage.

For the statue in India: do you have a picture, an article describing it, anything? How do we know it's an ear of corn and not some other object resembling it?

For the mummies: please read the article: it actually explains the tobacco traces very well. The cocaine presence hasn't been explained yet.

I think the did find a Roman Shipwreck off the East Sea board of the US. One which was proved to have been a case of "blown off course".