The Thalmor are supposingly gaining influence in Skyrim but from what i see they fail completely on their missions. Their failed missions include:
The plot against the college of Winterhold (Ancano is killed at the end)
The try to learn what is going on with dragons (they are ridiculed by the dragonborn and Esbern)
The distruction of the Thalmor guarrison at Northwatch Keep(during the mission missing in action)
The failure of Captain Valmir ( A Thalmor agent) to cheat you during the quest "siege on the dragon cult"
Their failures continue in Solstheim were they fail to find Stalhrim despite all their efforts
All i can say is that if they want to replace imperials, they must create better secret services