Hi MoZdk,
Although it is not exactly a "Make best move" button, there is indeed a way to advance the computer moves by using the usual move buttons (or the arrow keys if you prefer) as in examining the game.
At the top where you see the computer analysis you can click on the line you wish to see, it will load the variation into the list of moves, simply click on the first move in this variation in the moves list, and you can then use the controls to move forwards and back as usual to see what the computer had intended to do! Of course the best suggested move will change the deeper you get into a line, as the engine has more time to think on that specific move. (You can also click the gear icon beside the computer analysis to change the time it will think for, and allow it to calculate a bit longer before opening the variation it has calculated)
When doing game or puzzle analysis, I sometimes like to advance the game with best found move, in order to see how it could have ended.
Currently I have to read the move in the analysis 1st line (best), and then make the move manually.
It would be great if there was a "Make best move" button, in addition to the "Next move" button, so I could easier advance the game with best move.
Btw. thanks for the great updates to the puzzle section