I'm not quite clear on how Thane mechanics work, and thus I'm afraid to screw something up if do something wrong.

I am (was?) thane of all holds except Eastmarch long before retrieving the horn for Greybeards and without touching civil war line. Now I'm finally doing main quest, and Season Unending quest changed political status and Jarls of Markarth and Riften, temporarily for one of the cities, until I decide to join Legion. Now I'm wondering what happens to my thane status in those cities? I checked my house in Markarth, and my housecarl is still there. Then I went to have a chat with the new jarl, and turns out, there's a dialogue option to become a thane again, so I did, and got another blade of the Reach and a housecarl who was never gone in the first place. When in some indefinite future Empire re-takes Markarth again, I'll have to talk to the new-old jarl and have him name me a thane again? Are there any known bugs that can occur, like loss of Vlindrel/Honeyside, stored items, housecarls and their inventories or anything else?

Well I had this sort of problem as well, but that was in Winterhold. So I've got two Blades of Winterhold. But Winterhold doesn't have any house, so I can't really help you with that bit. I don't think you'll lose Vlindrel Hall or Honeyside though.

((I play on Ps3 so it may be different between the consoles and pc))
I don't think there is any side effect, maybe the stored items but else it should work as normal. I "lost" Breezehome temporarily since i switched Jarl and no side effects i just had to ask to become thane again and my house appeared normal. You also still own the house but you aren't having "Thane" title until you've spoken with the Jarl about it.
Couple of Jarls replaced.
My Stormcloak character removed Laila Law-giver(Riften Jarl) during season unending but already made her quest and later i put her back as Jarl and i asked to become thane again, and my house wasnt any different or at least i didn't see anything different about it. (Only done it once so not entirely sure though)
Maven(Imperial Jarl of Riften) is the hardest Jarl to speak with since sometimes she bugs and give her regular non-jarl dialogue.
Mostly the holds you conquer favors you and will just require "Known among my people quest" in which you help 3 or 5 people in the hold. (Knows this from my Imperial side Khajiit lvl 33)
In my opinion it would be better if people made themselves thane after the civil war is solved since the many gameplay changes and the possible bugs. And I'm thane in every hold.

All you have to do is go talk to the new jarl and you become thane again. You don't have to do any of the help citizen things or any other jobs again either. You'll also receive another weapon from them as well. (Blade of Whiterun)

You don't lose a house once you have a acquired it. The MQ will change who you get the house from if you have not acquired it.

The new leadership will reaffirm your status of Thane, if needed.

Thanks all.

Maven appeared to be bugged after all and giving me only one dialogue option regarding the horse (haven't done that quest yet), so I ended up deleting hours of game progress and playing Season Unending differently - trading Markarth for Dawnstar + allowing Thalmor byach to stay + compensation from Ulfric for Karthwasen. So Maven won't get to sit in the throne for a while, and stupid Dawnstar Jarl is also now replaced by someone so much more worthy.