Tes3Mod:Dirty Saves

If you add or remove mods from a game in progress, you're likely to end up with a dirty save. In brief, a save is dirty when it contains information that is mismatched with the current load list. The symptoms of a dirty save include: doubling, headless corpses, missing items, and crashes. 

Reference Problems
Most serious doubling-related problems are due to mismatches in reference IDs between the savegames and the mods they depend on. 
For more info, see Doubling.

World Map Corruption
When mods are added to the game, the world map is updated to show any new landmasses those mods have added. However, those landmasses are not removed when the mod is removed. 
For more info, see World Map.
This problem does not affect OpenMW, which regenerates the world map on the fly.

Clean Save  
In addition to using Wrye Mash on the savegame file itself, there is a procedure to take in game to prepare a save game for mod changes.
Move your character into a small interior cell and remove all items and clothing from body and inventory onto the floor. Then save and exit the game.
This is called a 'clean save'. While it will not eliminate all problems, it is a simple enough precaution that all players should habitualize this practice.
Certain mods may describe in their readmes additional procedures to take when desiring to add it to or remove it from an ongoing playthrough.

Altering inventories and spell lists for existing NPCs
Mods that change statistics, inventories, spell lists, etc. of already-existing NPCs will not, in most cases, update the respective NPC (especially their inventory or spell lists) if you have already interacted with this NPC. This problem happens because the NPC's data is already stored in your savegame and is therefore unaffected by the changes made in by the mod. You could apply these changes manually, but this may be extremely tiresome if many changes were done. Wrye Mash, on the other hand, provides an easier way of doing this, if you accept some restrictions for these updated NPCs.

If the NPC is a merchant of any type his/her inventory/spell list will be reset, and all changes according to the plugin's data will be done; this also means all items you have sold this NPC will be lost.
All disposition data for this NPC is lost, meaning it will be calculated again when you first interact with him/her. This may be of low consequence if you can easily raise an NPC's disposition, or if it is a guild fellow and you already have a high reputation within that guild.

If you can accept these two restrictions, the following steps are necessary to alter NPCs using Wrye Mash:

#Create a list of the NPCs that have been altered, the Construction Set is the best way to do this. You only need the Object IDs and the names of the NPCs, all other informations must be removed from this list. Object ID and name must be separated by a tabulator, which is the default for lists created by the Construction Set.
#Start Wrye Mash and change to the "Saves Tab".
#Right click the savegame you want to modify and select the "Remover" option.
#Now select the "Edit Removers" option and it will bring up a small GUI were you can add all lists containing objects you want to remove from your savegame.
#Add the list containing the altered NPCs and close the GUI.
#Finally, right click the savegame you want to be modified, select the "Remover" option, and right click the name of the list you have previously added, ignore the warning by clicking "OK". 
# Optional: you can remove the list you have used from the GUI since it is no longer needed.

This procedure will remove all listed objects from the savegame, and the next time you interact with a modified NPC he/she will have all changes introduced by the plugin.

Notes:
This method can also be used for containers whose inventories have been altered by a plugin. For creatures, this method in not necessary since every newly spawned creature will have its data modified accorded to the plugin.
If you want more information on this topic, read the "Remove" topic in Wrye's FAQ.