Kate at the joint where the walls join the floor in the shower, for the same reason as the corner joints in a steam shower, they really don't need to be caulked. There's a membrane that keeps the shower floor from moving with (or against) the structure, so there should be no reason for that joint to crack (unless this is s solid shower base). If the corner joints in the walls aren't caulked (and this is a conventional shower), then yes, use a utility knife, carve the grout out, and then use a siliconized latex caulking from the same manufacturer as the grout in the same COLOR as your grout, to caulk them.

Old caulk can cause problems. I've never seen caulk "crack" though. I have seen, when it is put on too thick, too much at once, or when it's put on an unclean surface, or put on a surface that was previously caulked with 100% silicon... In those instances I've seen it pull away from one side of tile. Normally due to shrinkage as it cures. But I've never seen the bead itself crack. For deep gaps you can use foam backer rod to "fill" part of the depth of a deep gap. Then you can caulk over the backer rod. New construction it could be house movement, caused by wood shrinkage. The baseboard is shrinking in the dry, less humid winter months, and "pulling up" away from the floor. If the caulk failed due to shrinkage, then you can sometimes go over it with new caulk and blend the two applications together. But it's hard to diagnose if it's excessive house movement or bad caulk. Since you've caulked before it's probably not operator error. If the caulk was bought recently at a store with good product turnover then the caulk was probably fine. So it could just be the first-year construction settling in during a dry winter.

The most common reason for cracked or flaking unsanded grout that I see is using unsanded grout in joints that are are too wide for unsanded grout. The second most common is the one Bill mentioned, mixing the grout too loosely. Too many guys do that, some get away with it, some don't. That can occur with either sanded or unsanded. Those two will normally result in cracks showing within a few days of installation, as they are drying cracks, caused by the grout shrinking as it gives up water in the curing/drying process. Cracks that show up later are usually structural, caused by the floor flexing, or as I've seen in a couple of situations, using mastic on floor tiles instead of thinset. Grout bags give a recommended amount of water to add per bag. But it's usually a partial bag mix, so that may not work well. I mix my grout a little thicker than most guys I've seen, but one thing I do is mix it a longer than most guys mix there grout, then I let it slake for the proper amount of time. The irony is that by mixing it longer, which happens to be for the recommended amount of time on the bag, you get a better mix. And the grout, when mixed to the proper consistency and mixed for the proper amount of time, spreads like buddah. There's no need to add extra water to loosen it up. Mongo

Curb movement like that is typically from a wood-built curb (stacked 2-by lumber, for example) that is absorbing moisture and expanding/swelling. How is moisture getting to the curb? Could be one of several things. Not sure how conscientious the installer was in terms of making sure the shower pan membrane is sloped (versus laying the membrane flat on a flat subfloor), or how he detailed the membrane over the curb. It's possible there are nails through the top or inside faces of the curb (and thus through the membrane) and moisture is getting through the nail holes. It's possible that he built you a perfect curb but used wet pressure-treated wood and the PT wood is warping as it dries. Or your house is on a slab, and he put the wood right on the slab. Moisture through the slab is causing the wood curb to expand. So it could be one of several things. It should be fairly easy to diagnose though, as the tiles are popping off on the outside face of the curb. They'll have to be removed eventually to diagnose and repair. When they are removed, take a look to see what's in there. Post photos if you can. To give you a bit of an education as to how a typical CPE-membraned shower with a wood curb is built, check out Harry's pictorial. Note that Harry's membrane is "draped" over the wood curb. That there are no nails/screws on the top or inside face of the curb. That the lathe (wire mesh) is bent in a "U" shape and it's simply the inverted "U" bends that hold it over the curb. Again, there are no fasteners through the lathe and into the top or inside face of the curb. I have seen instances where the membrane gets draped over the wood curb, then the installer nails cement board on the three faces of the curb and tiles on the cement board. Not good. Again, nails through the membrane on the top and inside face are a no-no. I don't see screws through the bottom track of your door frame that go into the curb. That's good. Best, Mongo