The problem seems to be a combination of Samsung's MicroSD slot and SanDisk's super thin MicroSD cards. Both the Patriot and Kingston 32GB MicroSD cards are noticeably thicker (almost 2x) and both fit more firmly in my Note 2' and S3's MicroSD slots.
I also have the same problem when using only the SanDisk MicroSD card in my multi-slot card reader. I get card not inserted errors as well as cyclical redundancy errors, misc write errors, etc. This card reader was not cheap and I paid good money for it because I use it for semi-pro digital photography -- I cannot have a card reader messing up my photos. I purchased my SanDisk MicrosSD card with a full sized SD adapter (just because that's the one that was the best deal). Guess what -- the SanDisk MicroSD card formats, reads, and writes perfectly fine when using the full sized SD adapter in the same card reader. Neither the Patriot nor Kingston MicroSD cards will fit in the SanDisk full-sized SD adapter, so clearly this SD adapter's slot is specifically designed for the significantly thinner SanDisk MicroSD cards.
So, I think the problem is that SanDisk made their newer MicroSD cards too thin, so they're not making constant, proper contact inside Samsung's card slots (and my card reader). My Acer A500 tablet has a better designed card slot so (at least so far) the SanDisk MicroSD card isn't giving me any problems in it. Likewise, my Patriot Class 4 card that's now in my Note 2 is not exhibiting any of these problems because it's a thicker card so my Note 2 (so far) seems happier with it.
Anyway, that's my current theory. I wonder if there are any other memory manufacturers who thinning up their card designs? So far, it's just been SanDisk that I've encountered this. Seems like most of the people here on this thread are also having problems with just the SanDisk cards.