Getting sick of the speedrun yet? After I get the mirror from Jim Archer, I do part of the trivet puzzle. That's not a tough puzzle; it's just long. Then I open up the carriage house. I do the clock, mirrors and dominoes puzzles. All of those puzzles have the pieces in the same starting positions every time, making it slightly easier.
Should you put the mirrors in place before doing the domino puzzle? If you put the mirrors in place first, Nancy says a line about letting light in. If you put the mirrors in place second, she doesn't say that line, but there is a short scene of light being let in, and not reflecting on anything. As it turns out, the scene is about one second longer than Nancy's line of dialogue, so you'll want to put the mirrors in place first.
Going back through the start of the game, it appears the matching puzzle in Topham's is randomized. If you save and reload, all the pieces switch places.
Also, it helps to zoom in on the cat, before giving the cat the mouse. This is opposed to taking out the mouse, zooming in on the cat, then giving it to the cat. That's because the cat's head moves, and it needs to be in the "up" position for the mouse to appear at its feet. This doesn't save a lot of time, but every bit helps!