First, Ryan: yes, I kept it out of the post above because I want to write one big post about the whole Russian grammatical unti “одушевлённость” and write about what counts as having a ‘soul’ in Russian, and what doesn’t. Now, in your example, everything is right – and yes, the rule is the use the form for genitive plural also in accusative plural for animate objects – but here there’s another thing going on, too! “Дедушка” is a male animate noun, but has the ‘outer’ form of a female noun, so a better example sentence would be something like: “Я вижу мужей и жён” (don’t really know when someone will use that one, but hey – it’s the grammar that matters!).

Petr – of course Республика Татарстан is not an animate object (I put the word Tatarstan in genitive above, it shouldn’t be, I’ll fix it right now). Here we’re dealing with a case of the “карта чего?” [a map of what?]. And for female singular nouns there’s no difference in accusative between animate and inanimate. So “вижу карту” and “вижу Анну” it is!