You can sprint using the Aux1 key.

Shallow water no longer instantly nullifies fall damage! Slime blocks are a good replacement. (or cloud armor, if you're fancy)

Leaves can be climbed up. This also makes them useful for breaking falls… as long as you don't hit a log underneath.

Slimes can steal your items. They will digest them after a few minutes.

The recipe book in the inventory is your friend. Click on an item twice to see what it's useful for.

Clay is very plentiful underground, so bricks are actually a sensible building material.

Ores start appearing at much lower heights. Iron start at about Y -200. (If you're starting a new mine, you can grab some iron from others to speed up the process).