Matching
Instead of forcing matches, allow the board to run its course and matches will happen eventually by themselves. Continue matching on the outside and controlling the board and eventually numbers will come together.
Previewing moves
Drag slowly in a direction to preview what will happen with the tiles. If they are going to merge, the tiles will appear to overlap. If they will simply move, the tiles will slide over. Use this preview to decide if that move is your best. Drag back to your starting location after the preview to avoid actually executing that move.