I find myself really wishing that selections would stick. They do sometimes, but not always

I'm not totally sure what you're asking for here. Are you saying you'd like to select an improvement then be able to hit the build button consecutively and be able to fill the empty tiles with the same improvement? If so, it sounds reasonable, but I don't use the build button much, if ever.

You can do pretty much the same thing by double clicking on the improvement in the project list. Double clicking on an improvement in the list selects and builds the improvement on the current tile and then cycles to the next free tile. So you can simply keep double clicking and you'll build that improvement on as many free tiles as you want. Isn't this what you're trying to do?

I understand where your coming from it gets to me at times too. Say you are wanting to build three market centers. You click the tile you want then the market center and build. When it goes to the next tile you have to reselect the market center to build sometimes. And factories never seem to stay selected when switching tiles. I've learned to deal with it though, and thanks for the double click advice, I always forget about that.

Actually, sometimes I've seen the game leave the same type of building selected when the build button is clicked. It's not very reliable, certainly, but it does happen.