There are two kinds of dirty edits.
1. Harmless unintentional edits that just annoy purists, and are a general sign of an unpolished work.
That's simply done by wiggling the mouse a bit while selecting a vanilla object to examine or copy it. The object is moved in the CK and its new position is saved in your mod.
To undo those edits you need to actually find them, i.e. you have to view your mod regularly in TESVSnip (or the Details function of the File/Data menu) and keep track of what you actually changed and what not.
The FormIDs are very helpful here, in the CK it's the minimized column next to the editor-name. Sort By FormID. Everything that starts with 00 is vanilla everything that starts with 01 is from your mod. There is some vanilla data that always carries over to mods, but when you make a change in a cell you never actually wanted to edit, that's obviously an unclean entry. To delete it use the DEL button in the CK's Details menu or TESVSnip.
2. The harmful ones that can break savegames.
Do. Not. Delete. Vanilla. Objects. It's a common beginner's mistake to simply delete everything that is in the way of your mod, but those objects may still be refered to by your user's savegames, and when their game tries to respawn the contents of a chest that no longer exists, the game will crash, this could happen weeks after installing the offending mod, so it's very hard to track down.
For every deleted object, your mod contains a deletion entry. In the CK's Details menu sort by the "Deleted" column to see anything your mod is about to delete. Now select them all and press DEL to delete the deletion info. Reload your mod, and use another way to get rid of those objects, (move them far below the ground, re-use them on another place, put them in an area that is unreachable for the player etc.)