Some of his damage is accidental because he's a kid and a human. That's fine.
Some of his damage is accidental because he simply doesn't pay attention. This isn't precisely desirable, and we'd like to change it, but we understand it.
Some of his damage is not accidental. This is not OK. (eg - I am trying to fix the closet doors after repainting the room. They are broken because he pitched a big fit and slammed the door, breaking the slider and the spring fittings).

The bigger problem though is that he absolutely doesn't care when he breaks or damages something. His responses are to 1) shrug and say something along the lines of "So what?" or "I don't care," 2) shrug and say "Well we have more of them" or "Buy a new one" or "Ceph/Dad can fix it," or 3) cry and call us mean for asking him to help with the cleanup or to do it himself

I can handle that he's more accidentally destructive than some other kids. But the attitude is really p1ssing me off, and the breaking/damaging during hissy fits needs to stop.
Any thoughts on how we get him to better respect the home and the things in it?

If it affects your advice:
He's currently not taking very good care of himself or his own personal possessions either... For examples: He had a nosebleed the other day and was mad that we told him he had to go into the bathroom to tend to it instead of letting blood run all over his face and clothes. DH collects sports memorabilia and SS asked for some of the hockey cards; DH gave some to him and gave him sleeves to put them in, but SS shoved some of them into the back of a desk drawer and kicked the rest under his bed.

He was pretty much destructoboy when he was about 8, but then was MUCH better and did almost no damage for awhile. But in the past 6 months, it's out of hand and there's a lot of attitude about it. So it needs to be dealt with somehow.

You ladies have the best advice for EOW parenting of kids with behavioral troubles :)

Neither of my boys was especially destructive, which is a minor miracle considering their issues. Or maybe it's my standards that are unusually low? ;-)

But in case this is any use -- I always try to give them a way to make it better. Involve them in the fix -- ex. HELP you re-hang and repair the door so they can see how long it takes. In addition to the 'pennance' of the fix work, there's the 'redemption' aspect of undoing their own wrongs to the extent possible. I'd say this is especially important in the 'hissy fit' type destruction.

One other parenting tactic that has been wickedly effective (evil grin) at willful misbehavior. You start with a look of shocked disbelief, followed by quiet horror, then more shocked disbelief. (You can't believe he has done something like that...) Then a few disjointed words about how surprised you are at his behavior... you can't believe... you just don't know how he could... (It's important that you're not too together on this.) Then something to the effect of how there will be serious consequences -- you don't even know what do to for an offense like this... But he needs to go to his room now and think about it. And you're going to go to your room and think about how to handle this... (shaking head) You just don't know... Of course, will have to confer with Dad when he gets home... Just can't imagine...

Now at this point, assuming the kid has a conscience, you've got his attention. I'd let him stew for about 45 minutes or so with no TV, no Computer, no games. (Gives you time to craft a really good response as well.) Then call him down for a calm, quiet talk. Ask him what happened that led to the incident and do very little talking. If what you hear is excuses, it's back upstairs for more contemplation. But if it's genuine remorse and a decent understanding of his behavior, I'd then ask him how he thinks he should be punished. (Odds are good it'll be something harsh!)

That one worked miracles on my two! Of course, I only had to use it once or twice on each of them. Would have worn out with more use ;-)

Not that it helps to hear now, but it gets better when he gets a tad older. DS now 33 , I was not sure I was going to survive and he did have a bit of new attitude problem to go with it at about his entrance into Jr High. He is ADD only.

He spent many hours working off something he broke. Nope, he did not mean to break it, did not do it 'on purpose', but broke and needs fixed is still broke and needs fixed. Dad had him 'help' in the workshop to repair and DS did lots of mowing grass (for a couple older neighbor ladies).

DS also wanted the collectible stuff but when he got it I always placed the items in my hutch ...kinda, yeah, cool, but lets keep it in here. Partly because he would 'forget' and stash it under the bed on cleaning day along with his socks, partly because he would get implusive and trade it off at school.

I'm not sure there's any easy solution/answer I can pass along. I just kept at it and we took each incident day by day, offense by offense. Some of the things (like the workshop) we did might not be possible for you and he lived with us fulltime. One good thing that did come out of those years, DS grew up to be very good in a workhop and it has come as a plus as he puts all he learned into practice as a home owner himself now. He just redid all his kitchen cupboards and made his own fronts LOL.

I think the important thing for us back then was always being sure we did not let him get away without being responsible for his actions. The more he had to help fix and/or help pay for replacement the harder he thought before acting impluse urges.

Sorry, I have no idea of how to handle the 'I don't care' or the cry tactic he's using. Are you giving him a bit of time to settle down before broaching clean-up and/or 'lets talk about this' ? That likely does not sound quit right way to put it...we found it better to give him time to sit in his room and walk away for a spell and then 'now let's get this cleaned up' or the 'okay, now we have to get this fixed', or even the 'I think it's time now to go talk to your sister about breaking her _______ and let her know how really sorry you are'. KWIM?

But you're in a tougher timeline with going between homes than in my case.

I do think, though, you've gotten some great advice. I especially like Sweeby's idea of really making sure that SS is involved in the fixing or repairs. Let him see exactly the time involved. Does he get any kind of allowance? I would not hesitate to make him be (at least partially) financially culpable. If he breaks something--in a purposeful, destructive way--then he can do extra chores to "pay off" what he owes.

IMO (and you stated this, as well) it is one thing to be more accidental, less cautious, etc. Breaking things or being careless in that manner is probably par for the course with ADHD. BUT if he is deliberately slamming doors, throwing things, etc. and breaking them, he needs to be given some clear consequences.

I think some of it may too be his age and his gender. My dad's girlfriend's son is 13 and he seems so oblivious to me at times, like he just really has no clue. He'll dump his shoes and stuff wherever, and then blink and stare when asked to put them elsewhere. He'll leave dirty dishes out, turn on the tv REALLY loudly when people are in the living room having a conversation....just that typical adolescent stuff.

I have spent the summer volunteering with my daughter's swim team, and I got to know the kids pretty well. Let me tell you--the difference between the 11-14 year old GIRLS versus the 11-14 year old BOYS is unreal.

In the 15-18 age group, they seem more on par with one another.

So I think some of this is a boy/age thing.

Sweeby, part of it may be in reaction to our upcoming baby. But since it was happening for a few months before he even knew about the baby, it isn't 100% baby-related.

The penance/redemption idea doesn't seem to be working for us.
An example from a few weeks ago to show how it goes:
SS was mad because his mom and her DH were doing something that weekend but he was coming to our place. So when DH picked him up, he was miserable in the car.
When they arrived, I said (oblivious to this situation) "Hi A__! How're you?" He gave me a sour look and dramatically kicked his muddy shoes off right into the wall. Then he chucked his backpack onto his muddy shoes and ran to his room, presumably to sulk.
I asked DH what that was all about and he explained that SS is mad that he's here instead of doing what his mom and SF are up to this weekend. DH waited about 15 minutes and went in to talk to SS about our weekend plans. SS seemed to have mellowed out, so he also said "When you come out, I'd like you to wash up the wall that you kicked your muddy shoes into. Your backpack will also need a wipe, since it's sitting on your muddy shoes." I heard DH say it, and it was not in an angry or accusatory manner, it was just matter-of-fact.
SS's first response was that he doesn't care that there's mud on the wall or his backpack. DH, still calm, said "Well, we care, so you need to clean it up." Then came the tears and the sobbing that we're incredibly mean because we're making him clean up stuff he doesn't care about. DH, annoyed now, said he could stay in his room and read until he was ready to clean up his mess and be pleasant.
He eventually came out because he was hungry and wanted to watch TV. He pouted while he cleaned up the mess, and to be honest, did a crap job of it. I even got him a fresh bucket of water after the initial wipe-down, and very very calmly and patiently showed him how to wash it ALL off. But he mostly just scowled at me and spilled water on the floor.

This is almost always the pattern.
He breaks/damages/messes something and when he is asked to please do or help with the cleanup, he pulls out one or more of these responses.
Are we approaching it wrong? Could we have dealt with the muddy shoes incident in a different way?

Honestly, that's exactly what I would have done, and probably, exactly how my older son would have responded. (So it's not perfect!)

Sometimes a simple "Who is it you're mad at?" question can help him realize that he's been sulking at an innocent party -- ut it'll probably take a few months to get to the next phase where he realizes Oh - I'm not mad at them. So don't be mean to them...