Thanks for the comments so far. I'm not a structural engineer, but I'm 99% sure I know why the floor is sloped. The house used to have a 2 story back porch, but somewhere along the line it got closed in and converted to a kitchen below and bathroom above. They just framed around the outside and sided. The floor still slopes backward away from the main building. It isn't like it is going up and down an inch with the seasons. It was just purposely built with a slope. So, I guess my question is what method of leveling the floor (if any) will help minimize any seasonal expansion/contraction? Sistering additional boards to the joists to level and then new plywood? What thicknesses? After it's level, is a membrane the way to go? Does adding 1/4" cement board under a membrane provide additional protection or is it just a waste since the membrane will move above it? As for sizes, yes the kitchen is significantly larger than the bathrooms. It also has an attached pantry/laundry room that we would like to carry the tile through. That is why the potential movement has me a bit concerned. It has gotten a lot more stable since I regraded around the foundation and extended the downspouts out farther from the house. I will be putting plastic down (after I get all the junk out of there.) Still, a dirt basement is always going to have humidity swings.

Weedy gave you pretty good advice. A typical "fail" is that the cement board is simply nailed or screwed down over plywood. As Weedy mentioned, the cement board should be bedded in thinset, then fastened to the plywood with nails or screws. The bed of thinset simply acts as a void filler between the cement board and the plywood. It prevent micro up and down movement of the cement board. That micro movement can result in popped tiles and cracked grout. With a basketweave, it's be common for the grout to crack and pop out of the joints. But for the individual pieces to crack? Being small, they can usually accommodate some movement in the substrate. I'd take a close look and see if they are indeed cracked, or if perhaps grout got stuck in any veining or fissure lines in the tiles. If the tiles are indeed cracked, that's a problem. It's very difficult to effectively reinforce a floor from below. Floors can flex in one of two ways. The joists can be undersized, so you're getting flex along the length of the joist. Or the plywood can be undersized, so you're getting flex in the plywood between the joists. IF the joists are properly sized, the plywood sufloor should have ben 3/4" thick tongue and groove plywood. Covered with 1/2" thick cement board, thinsetted and fastened in accordance with the manufacturer's installation instructions. As far as the grout in the wall/floor joints all cracking, as fori wrote, those corner joints should be caulked and not grouted. Caulk can flex with movement between different planes. Grout, being rigid, will crack instead of flex.

Could be. One way or the other it's obviously something that gives it its water resistant properties. I don't know for sure, though. What I DO know is that thinset will bond much better to plain old white sheetrock. As for the original question, I don't see any problem with putting glass over sheetrock.

Hi Nola - I assume you're asking about Sumi-e glass tile, correct? When I talked to the tile vendor and tile maker (Walker Zanger and Lunada Bay, respectively), they were pretty adamant on installing the glass tile on cement board. The Lunada Bay guy said that the tiles may or MAY NOT fall off, and if you've gone a year without anything coming off, you're probably fine. THAT BEING SAID, I just googled and saw this guide that says you can install glass tile on drywall if it's an area that doesn't get a lot of moisture. Has your contractor installed glass tile before? Glass can be persnickety to install and there are special considerations like using a latex-modified thinset (preferably white). I know that the sumi-e tile you want to use is not inexpensive, so you want to make sure your contractor has a lot of experience with glass tile installation. Hopefully Bill V. will see this post and confirm that drywall is okay. Here is a link that might be useful: Glass Tile Installation