/u/CommodoreCoCo has covered the Mexico angle, but I presume that the ships off Brazil stems from Robert Marx's claims of discovering one in a bay near Rio de Janeiro? The major facts are outlined in two NYT pieces, here and here. There was no actual ship found, Marx, a treasure hunter by trade, simply claimed to have found a large number of "roman" amphorae in the bay. This was based on a review of pottery sherds he provided to an actual academic, who made a tentative declaration of resemblance 3rd century CE North African amphorae. He then got in a bit of trouble for not reporting all the items he had auctioned off from previous treasure hunting, leading to a revocation of his permit to dive in Brazil and a temporary countrywide halting of treasure diving in general. Marx claimed a cover-up.

So there was never a ship. What we have is a few fragments of pottery which Marx claimed to be 2nd Century BCE Roman and an archaeologist said might be 3rd Century CE Roman-North African. The problem is that neither Marx's declaration nor the academic assessment have ruled out that these amphorae fragments might have belonged to amphorae-style jars used extensively in shipping in up until the modern age, including some actually made in South America.

Basically, amphorae does not equal Roman, and heresay does not equal conspiracy. There is no evidence of a Roman ship in Brazil, only broad assertions by one man.

I'm assuming you're talking about this statue?

As far as "anamolies" that the internet loves to pick up and have their fun with go, it's actually one of the better ones. It's not as blatantly a fake, nor is it a misinterpretation of something normal. That being said, it remains a single artifact from a relatively late burial. Academics of any sort don't make conclusion off of single data points. Of all the possible explanations, actual Roman contact would leave behind the most evidence and yet manages to have the least, with a grand total of zero other supporting facts. Even an anecdotal claim that it was planted is more evidence than the Mediterranean contact theory has. And that's without making any claims the feasibility of such a voyages. Even if it was definitively possible for the Romans to have crossed the Atlantic, there would still be no reason to claim that they did.