What is the span and the spacing of the floor joists? Google "deflectolator" (GW doesn't allow links) and plug those numbers in to see if the floor framing is sufficient to support tile.

Then review your floor construction:
Plywood: You need 3/4" either plywood or OSB on top of the floor joists. Verify how thick it is.
Blueboard: Are you sure? Like drywall? This should be cement board. There should be thinset between the plywood and cement board, and it should be screwed in every 8". If your contractor really used blueboard, the job needs to be torn out and redone.
Thinset+tile: at least this is right.

This sounds like a major fail to me. Report back on the details above and we can help further.

Plywood was 3/4", and then Durock cement board (apologies for the confusion, blue board was on the walls)

OK, glad it wasn't blueboard. :-)

Did you check on joist spacing and deflection?

And was the Durock installed with thinset below and screwed every 8"?

As far as the grout cracking between floor and walls, it's a minor problem compared to the flexing--it'll always crack there which is why it's not supposed to be grouted at all. It should be caulked.

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.