Corners should be caulked, not groued. The bathroom we are remodeling now had grout in the corners. There were some very small hairline cracks and when we tore out the tile, (green sheetrock underneath, another no-no) there was some black mold there. We assume the cracks allowed moisture to seep in and thus the mold. Tore it all out, sprayed for mold, put a moisture barrier up and cement board over the studs. When we tile it, we'll use caulk in all corners. What should you do? You can dig out the corner grout and replace with caulk. Digging out grout is not fun nor easy. You have to be careful not to chip the tiles. Cleaning grout, there are many products out there that claim to clean it, none worked too well for me. I have a powder blue floor tile with white grout that is going to be replaced with gray tile and gray grout. But I did find the thing that cleaned it best was oxy clean and water, soak the grout well, scrub hard and rinse. It did a pretty good job of it. Another option is to buy one of the aqua seal grout colorants, never used them but they get good reviews. My original plan was to use the colorant on my white floor grout, but we decided we didn't like the blue tile anyway, so we're replacing it and this time, I will use gray grout. Pretty as white grout is, I find the older I get the less I want to spend my time on things like scrubbing grout.

I have always wondered about the caulking of the corners and bottoms of my backsplashes, (which my contractor does not do). When do you do the Caulk? Before the grouting? This way, the change of plane area that needs to be caulked stays free of grout. If you grout first, instead, how do you keep the grout out of the lowest row and the corner where the caulk is supposed to go?