What do you mean by your question, "best continent for mammals"? Which continent has the most mammal species? Which has the "best" species? Which is the best for seeing the most species in the wild? Which is the easiest to see species in the wild? There are a load of variables in the question.
The question is entirely subjective and you can treat it as you like. I’m obviously I’m not asking people to count up the mammal species on each continent though.
In the wild, I would probably say Africa, as I don't think any other continent has so many large (And small) mammals in such large numbers, and judging from what I have read these numerous ungulates, carnivorans, and really much else are readily viewable. For captivity, Europe is probable the best, as, judging from zootierliste and the zoochat gallery, there seems to be way more species in zoos in europe as a whole, and especially some juicy rarities at the likes of Pilsen, Prague, the Berlins, Cologne, Moscow, etc. (It is quite enjoyable reading of those juicy rarities on the thread by @amur leopard yourself) Keep in mind that I have been to neither continent, this is just what I have read
I chose Antarctica because while no land mammals live there, the ones that do live there aren't as disturbed by humans.
If you are defining the best continent in terms of mammal biodiversity then I believe it would be North America and in country specific terms Mexico which would have the highest rate of mammal species.
Indonesia has the most species, by far, and the most unique species. Mexico is generally ranked 5th, after Australia, Madagascar, and your own Brazil
Yes it seems that you are right, I remember when Mexico was ranked 1st but it appears that it has dropped a few places now. Still 5th place for mammal biodiversity is not too bad for a country but of course the challenge is to conserve that incredible biodiversity. It seems that none of the top 5 megadiverse countries are doing as well as they could with conserving their mammalian biodiversity.
It probably dropped as more species have been discovered in the others; Mexico is much easier to explore, and has had a lot more explorers! Same with Australia.
Definitely think that is a factor, but I'm sure there are still mammals waiting to be discovered by science and particularly in the South-East.