What to do about a tile floor that with globs of thinset
I've never seen tile installed this way. I've seen installers glob it down, but then trowel it out. Tile needs to be installed on a flat, sound surface or  it will "bend" and will break or loosen over time. what type of guarantees did you get from them? I'd put them on notice and get them out there when the next tile pops off.