Can I takeback a move if I make a mistake or if there's a mouse slip? (Dasher)

Yes, but only if your opponent agrees. You can request your opponent allow a takeback. They can either grant your takeback or ignore your request.

You are not obligated to grant takebacks even for obvious mouse-slips. You can refuse takebacks in all situations or allow them in some. It is entirely up to you.
To request a takeback from your opponent:
Dasher interface: Above your board is a button in the shape of a brown ball with a white arrow pointing to the left. When you click this button you get the options for 1 move or 2 moves.  Click on one of the two options.
This button is also used when you want to accept a takeback from your opponent.

The request can be ignored by simply continuing play.

Alternatively you can type 'takeback'  on the command bar under the Main Tab of your Console or '/takeback' under your Game chat window.
To accept the offer, your opponent must also type 'takeback'
To ask to take back two moves instead of one, type 'takeback 2' 

 Note: In tournaments run in the Tomato system you can not do takebacks.

For more information read "help takeback"