Baby uses a dictaphone to record conversations that he has with other people and later mixes them into songs, much in the same way that he himself hears phrases from the television or other people and uses them in his own conversations later. He's a human sampler.
Baby's reluctance to speak and ability to read lips are never explicitly explained, but are obviously due to spending his life listening to music in earphones and being raised by a deaf foster father. His need to audibly converse with others has been limited.
Baby and Debora's first date starts at a laundromat. Laundromats are loud due to the noise of the washing machines, which helps drown out Baby's tinnitus.
Doc expresses perfect confidence that Baby understood his entire speech in spite of wearing earbuds through it all. They've already done a number of jobs together, so this has obviously come up before.
Doc says he and Baby first ran into each other when Baby stole his Mercedes. When Doc is killed by Buddy, what does Baby hop into with Debora as a getaway car? Doc's Mercedes.
Baby's seemingly endless supply of sunglasses and iPods are the spoils of his lifelong career as a car thief.
At first it seems like a stupid move for Baby to never cover his face (besides wearing big sunglasses) like the rest of the heist crews, thus leaving his identity exposed. However, as their getaway driver he needs his peripheral vision - a mask would get in the way of him properly doing his job.
Misplacing a shotgun was just a matter of time for JD - he was the only armed crewmember who did not wear a sling to secure his weapon.
When the second robbery has the crew be forced to abandon their getaway car and force out a woman out of her car as a replacement, there is a small baby in the backseat. When Baby removes the child from its seat and hands it over to the mother, Bats reacts angrily despite it only taking a few seconds. Bats seemed to have wanted to use the child as a hostage or just not care at all if the child got hurt or abandoned when they switched cars again...or worse.
When the women says she has a child, Bats angrily yells "I got one too!" Assuming he was telling the truth, let's hope he's a Disappeared Dad.