I recently verified Skyrim's local file cache through Steam, but I am running into some issues... It resets some of the positions of some characters, such as Idolaf Battle-Born and Adrianne in Whiterun talking like when you first enter. Or the All-Maker stones on Solstheim having the green sheen on them and "hypnotizing" my character even though I finished the Main Dragonborn Quests and played for over 350 hours.

Is this just a ramification of verifying or can it be fixed?

AFAIK, verifying the cache only check to make sure all the required files are present and not corrupted/modified. All the journal information is on the save files and not touched.

Have you been using quick saves/loads or auto saves? They may not save every fine detail and may lead to issues.