Returning to Nexus
This is less of a trick and more of a reminder: You can return to the Nexus at any time via the game's menu. Place your cursor on "Map" and press your confirmation key. Very useful if you get yourself stuck using the swap upgrade.
When swapping tiles, you can re-select the same tile you just swapped, even if it would place a solid tile beneath you. Basically just a time save.
Out-of-bounds swapping trick
The tiles on the very left and top sides of the screen can be walked on if you swap to them. Handy for bypassing solid obstacles. However, the same doesn't apply to the bottom and right tiles.
Screen transition trick/Wiggle trick
You can get through solid tiles with this trick. Perform it by rapidly transitioning screens from side to side while holding up or down.
Falling in a pit glitch
This trick lets you warp around the Nexus. When you are falling in a pit, if you rapidly access the menu and warp to the Nexus, the game will place you on the screen with the same coordinates as the screen where you fell. Mainly used to get the secret 49th card.