If you match four pieces instead of three, you’ll be awarded with a special version of the upgraded piece. This is worth more points, and can be matched with non-special versions of the same piece.
When you get a diamond and there isn't anywhere great to put it at that moment, store it up in the top-left corner until a good match appears.
Try to have a corner of the screen where you trap your bears - don't let them simply roam around the entire town.
The storehouse (up in the top-left corner of the grid) can be used to store items for later use. The best idea is to always store items that are higher up the item hierarchy than whatever is already there.
Use the coin store when you really need to. You only get seven of each item per game, so it's worth waiting until you've very nearly dead before resorting to this.