Playing Skyrim regret-free

The UESP wiki, 'Quest Timing' article has a detailed list of quests (and notes about those quests) that will have a significant impact on other quests and the game, in general. Some of them are due to bugs, and some are because they are designed to be that way.

It also recommends if a quest has to be done early or be postponed before/until another quest has been finished or another game event has happened, to prevent bugs or a negative impact on other quests, or the game.

The whole article is too big to be included here. I'll be adding some of the most notable quest categories and the quests under those categories related to your question:

Quests to Do As Soon As Possible

• Blood on the Ice
  Why: The Necromancer Amulet is a Legendary-quality item very useful for low-level spellcasting characters, especially those interested in Conjuration, and can be sold for a lot of gold for a low-level character. There are numerous glitches associated with this quest, and the best fix is to start the quest as soon as possible and complete it all at once.

• The Forsworn Conspiracy and No One Escapes Cidhna Mine
  Notes: ...if you side with the Stormcloaks in the Civil War and if you complete Forsworn Conspiracy before Compelling Tribute and then wait until after Compelling Tribute to start Cidhna Mine, it will become unavailable permanently. It is also possible to have the same effect result from completing Forsworn Conspiracy, then completing Season Unending before Cidhna Mine, even if you have not joined the Stormcloaks.

Quests to Save for Later

• Dragon Rising
  Why: Completing this quest early ensures a large number of Dragon Souls by exploring, if the player is capable of surviving the dragon's attacks.
  Why not: After completing this quest, Skyrim will be full of dragons. Deferring it until you're in the mood to fight dragons lets you explore the world in relative peace and allows you to learn Words from Dragon Lairs more easily. Note that starting the quest will not cause dragons to appear; only after killing Mirmulnir will dragons start spawning.

• Joining the Stormcloaks or Joining the Legion
  Why not: Joining either the Stormcloaks or the Legion removes access to all the opposing faction's camps and causes "random encounter" fights to occur. Capturing towns has been known to break certain quests.

Quests that Conflict

• Lost to the Ages (Dawnguard DLC) and Mourning Never Comes
  Why: During Lost to the Ages, you are required to trek through Raldbthar, where Alain Dufont lives. If you kill him before starting Mourning Never Comes, you cannot kill Nilsine Shatter-Shield for the bonus reward in that quest.
  Why not: Alain only becomes hostile if you attack him, he won't defend the other bandits in the area. You can kill all the bandits but Alain, and complete Lost to the Ages without affecting Mourning Never Comes. Also, Mourning Never Comes is only available if you choose to join the Dark Brotherhood; if you choose to destroy them, you will never be given it.

The only major example of this that I can think of is that there is a segment of the main quest that is skipped if you resolve the Civil War prior to reaching it.

Similarly, your decisions during that chunk of the main quest can allow you to skip some of the more repetitive fort-conquests during the civil war if you play your cards right.

Other than that, and the obvious mutually exclusive choices (Stormcloak/Imperial, Blades/Greybeards), there shouldn't be any other dead ends.

I'm not aware of any major problems you can run into.

Most decisions with big results are fairly obvious, in some cases you even get told explicitly that a decision is final (and even then there are occasional "outs" that might help overturn the decision).

But some quests are broken in that finding the item-to-be-tretrieved before getting the quest can prevent you from finishing the quest.

Disclaimer: I don't tend to go on random killing sprees, so I can't speak on the effect of those on sidequests: their quest-givers might not be marked as essential and you could easily lock yourself out of some sidequests by doing that. The people essential to the main quests are essential and you can't kill them anyway.