Cathy

Dean is *okay* with the tape deck in Baby being broken? Oh, boy... Without any more context, I can see it meaning any of three different things...

A) The good.
Remember way, way back to "Dream A Little Dream Of Me"? When Dream!Demon!Dean confronted Dean about being nothing more than a shadow of John? "What are the things that you want? What are the things that you dream? I mean, your car? That's Dad's. Your favorite leather jacket? Dad's. Your music? Dad's. Do you even have an original thought?"

The car is still technically "Dad's" - but Dean has rebuilt it from scrap enough times that it's also his (and also he talked John into buying it so. :) ) The leather jacket is long gone. But the music... that cassette collection. He's been hanging onto it. But so far this season:

In "Mint Condition", Dean and Sam confronted and destroyed a metaphorical representation of John. (tl; dr: the horror movies were a symptom of Dean being abandoned to a series of hotel rooms - no Dad but here's HBO; also Matt Cohen in the "movie trailer"). Since it was a ghost, Dean was able to physically fight it - but ultimately they had to burn its link to the here and now, so it could go on its way.

Then "Nightmare Logic" featured this interchange:

DEAN: Can I give you a little advice? Let it go. The past is... There's nothing you can do about it now, so... it's just baggage. Let it go. You'll feel a lot lighter.
SASHA: Is that what you do?
DEAN: I try. Every single day.

He's moving on from John faster and farther than he ever has before. Letting go of the tape collection - willingly! without a word of complaint! - might mean that he's starting to explore the things he wants, the things he dreams. (From a shippy perspective, he apparently chose to spend the trip talking to Cas rather than finding some other way to play music - we know he's got an MP3 player and phones have speakers; Cas might be an essential component of those dreams.)

B) The bad.
Baby is a representation of Dean's soul. If a piece of Baby is broken - admittedly a non-vital piece, one he thinks he can do without under some circumstances - it might indicate that a piece of Dean is broken and he knows it, even if he thinks (or pretends) he's getting by. (Would he have been okay with not having music in the car if Cas hadn't been there to talk to? Cas's presence provides emotional stability.) Note that the conversation in the rest of the scene talks about getting revenge for Michael; I don't think it will be that easy.

C) The (maybe) ugly.
"Driver picks the music" very often works out to Dean claiming the space and the right to set the agenda; it's his car, he's driving it, he's in control of how things will go. (He wishes.) His pick today... no music at all, not entirely by his choice. Does he feel like he's going nowhere? Has no control? Is he accepting that circumstances are out of his hands? historically he hasn't been very good at that, notably recently he has been upset about the bunker being invaded, but he's been doing better about trusting Sam, Cas and Jack. Or is it a subtle hint that Dean is not actually the one driving - that Michael has been manipulating all the circumstances of these events and their attempt to go after the spear is part of his plan?

...again, without any more context, it's hard to say what's actually going on, and given that this is the mid-season finale I'm inclined to say "whatever combination of things works out to hurting the most" which could possibly be all three. But it's definitely not a throwaway detail.