Sometimes a quest might not continue, can't be completed, or a next quest refuses to start. Many of those issues have been resolved by the Unofficial Skyrim Special Edition Patch (USSEP), but if you don't have the patch or don't want it for whatever reason, there are ways to resolve the issue(s) by using the console. Although a developer's tool, the console provides console commands to solve issues with quests.

The Unofficial Elder Scrolls Pages[en.uesp.net] (UESP) documents all available quests in the game. See also Set a quest stage.

This guide will show you which commands you should never use, which commands can be hazardous if improperly used, which commands can be used with caution, and which commands can be used without any harm to your gameplay.

<questID> = the Editor ID of a quest
<stageNum> = stagenumber of a quest
<questVar> = a quest variable (postfixed with '_var')
<newValue> = new value for a quest variable, either boolean (0 = false, 1 = true) or integer
Use these parameters without the brackets.

You really should never use the following console commands regarding quests.

Syntax:
This console command, in most cases, will only mark the quest as completed in your journal, but actors related to the quest (reference aliases) may not recognize that you have completed a quest and may fail to give you a following quest or task.

Syntax:
This command will complete every possible quest in the game, not only the ones you have started. This will essentially complete the game, but this command may crash your game!

Syntax:
This command will start ALL quests in the game and will add all to your quest journal. Not recommended and may crash your game!

NOTE
If you are going to experiment with this command, you will have to be aware of some issues that may occur. I have experimented with this command and all eight tries resulted in failure, two freezes and six CTDs. During my last try on a new game with only the game's base files, I was able to save the process to a named save in the console (caqs_001.ess), although I first had to verify game files and two of the base game files had to be re-installed. Continuing the process with this save, I was able to do another save (caqs_002.ess). but continuing with the second save, the game froze again. Now, at least I had a save that I could research. In total 522 quests were marked as completed, but 32 were not. With the last save I could activate the Esc-Menu and have a look at the statistics. The 32 quests that were not marked as completed either were radiant quests or had the player perform some action which, obviously, is not possible when the command is running in console mode.
Could you succesfully run this console command? I can't confirm this, but at least you have to:

• complete all radiant quests, Thieves Guild radiant quests beint the most prominnet
  
• complete quests where you have to perform some action, reporting back to a quest giver, return an item to a quest giver or other actions when not in console mode

Dialogue and scene quests don't seem to be affected by this command. Most probably because these type of quests, which you don't find in your quest journal, can't be completed.

Syntax:
This command will instantly teleport you to the quest target, that is the marker on the map. It does not advance the quest, but it may bring you into a situation where you find yourself in the middle of enemies. Otherwise you might skip triggers or dialogues to advance through quest stages, or you might find yourself on top of a trapdoor.

Using this command after accepting a quest will in general not be that harmfull as it will teleport you in front of a door or cave entrance. Still, in some cases there might be a guard outside the door, such as Sunderstone Gorge or Driftshade Refuge. Be careful using the fast travel option to travel to the quest marker on the world map. In case of the world map, if you want to use fast travel, travel to a nearby safe location. Inside interiors do not use any commands that may teleport you to another interior cell if a location consists of more than one interior cell, such as the coc command. In that way you may skip important triggers and confrontations with other NPCs that might be important for the outcome of the quest. Also, do not use the movetoqt command inside interiors for the same reason.

Syntax:
Know that not all quest stages are properly or completely documented an various sites. Often stages that are set through triggers or dialogues are not documented at all, although these may be important for quest progress. If quest stages are not documented in full, you will have to do some research, either by using the Creation Kit or SSEEdit.

At the bottom of the quest pages in the UESP you can find a table with the quest stages. Below the table you may find a small list of stages that are omitted from the table because those stages are empty. This doesn't mean that those omitted stages don't have a function, as these can be set by another quest, by another stage in the quest, by triggers, through dialogues with quest aliases or through scripts. If you get stuck during a quest, consult the UESP quest page for reported bugs and possible solutions.

Syntax:
This command will reset a quest and set all quest stages to 0. However, quests that are marked as Game Start Enabled and/or Run Once can't be reset, which is the case for most of the quests in the major questlines. Then a reset will have no effect!

Syntax:
This command can be used to alter the value of a quest variable, either a boolean (true/false) or an integer (whole number, not decimal). This command refers to properties in Papyrus scripts attached to a quest. This command does not work for other data types than boolean or integer. Quest variables are postfixed with '_var'. Do not change the value of these variables unless you're absolutely sure and it is necessary to continue and complete a quest.

Syntax:
This command shows a list of active and completed quest objectives for the currently active quests. This command can be helpful in combination with the sqs command.

Syntax:
This command displays the stages of a quest and shows if a stage is achieved. If not, you will find the value 0.00 behind the stage, otherwise 1.00. It is not necessary for every stage to have been set to 1.00, and setting a particular stage may even cause the quest to fail or cause a different outcome than you expected or pursued.

Syntax:
This command lists all active quest IDs and their targets, and is useful for finding the quest ID for targeted quest commands.

Syntax:
This command will display all quest variables of the selected quest.

As for an example take a look at the quest Hired Muscle[en.uesp.net], part of the Companions questline.

The section Quest Stages mentions the omission of the stages 0, 1 and 200.

• Stage 0 will be set if you have completed the quest Take Up Arms and stage 1 will be set after talking to Farkas. Stage 200 activates a cleanup script and stops the quest.
  
• If stage 20 is completed succesfully, stages 30 and 40 will remain unset, but stage 100 will be set. Stage 100 will set stage 200 for cleanup.
  
• If you killed the target, stage 30 will be set and stages 20 and 40 remain unset. The quest will fail and stage 105 will be set, which will set stage 200 for cleanup.
  
• If the target of the quest was already killed (but not by the player), stage 40 will be set, which will set stage 250, meaning that all objectives have failed.
  
• Stages 20, 30 or 40 will be set after having returned to Farkas and talked to him.

If you take a look at the Bugs section, you will notice this quest has not been thought out very well. The target could already have died, the target is inside a location that require you to trespass, the target may already have been removed from the game, and even Farkas may be the target. Also some other issues are mentioned in the Bugs section.

In this quest the quest stages are linear, but this will not always be the case. For instance, if you are supposed to talk to an NPC when stage 50 is set. Depending on your choices in this dialogue, stages 20, 30 or 40 could be set, each leading to other stages above 50. The same could occur when a trigger is conditioned.

It may therefore be important to check the Bugs section of the UESP quest pages. If that doesn't give you an answer to the issue, you will be forced to do some research, preferably in the Creation Kit, as it provides far more information than SSEEdit.

(More examples to be added)