If you slide your finger left and right quickly when you're approaching clusters of coins you will be able to collect plenty and boost your multiplier.
Collecting Stars
Try and collect as many stars as you can early on in 'Coin Down' mode so you don't have to take so many risks in the later stages to pick them up.
More Points
You will get more points when you do a long uninterrupted voyage with several mistakes in short succession than an equally lengthy run punctuated by regular deaths.