During the flashback scene, one of the nuns mentions to Stick of Matt's mother not being deceased. This hint is based on the fact that during Frank Miller's run in the comics, in the "Born Again" story arc, Matt's mother Margret was revealed to still be alive, where she had run away to become a nun and is living under the name Sister Maggie.
This is the second live action appearance of Stick and the Hand, after Elektra (2005). However, the original Teenage Mutant Ninja Turtles comic was a spoof of Daredevil. That is why their master is called Splinter (pun on Daredevil's master, Stick) and their enemy is the Foot (instead of the Hand). This is a rare instance where a spoof received a film adaptation before the original.
The first time Matt uses sticks to fight (which would later become his weapon of choice)
A newspaper article featuring the Hulk regarding the Duel of Harlem from The Incredible Hulk (2008) is seen framed in the background of Ben Urich's office.
The wrapper bracelet that Matt gives to Stick contains a Hidden Mickey in the pattern.