If am going to rank his influence literally, I'll give it an A. Tobirama was a powerful shinobi and an adept fighter. His inventions was revolutionary, but they left a bittersweet taint on the series, bitter in the sense that some of his jutsu inventions was utilised against his the ideologies he left before he died. For example, we all know of the jutsu Edo-tensei, which was used by Kabuto has an addition to Obito's arsenal against the allied nations. Why we may find fault in Tobirama desire to create such a jutsu in the first place, his intentions wasn't predicated on disdain, but on the desire to improve the success rate of his abilities. People found out it could used in wars, and decided to refined it for that purpose, and as such immortalising the name, Tobirama. In a way, the jutsu established Tobirama has a genius, a great inventor, but at the same time cause people to find substantiable reason for its creation, since if he hadn't created it, Kabuto wouldn't have been able to use it.
In terms of his decision making, perhaps he made the greatest mistake which largely influenced the route the series took. Specifically, if he hadn't isolated the Uchiha clan, there wouldn't have been fractures within the clan standing-point on the village system. Of course he had good intentions when he isolated them, but his action made the clan a hotspot when it came to placing blames. Not a good idea if you trying to mitigate their curse of hatred. If you are going to quench someone's hatred, love is usually made the extinguisher.
All in all, this actions modeled the series greatly, albeit not in way that made him a source of people references. Everybody loved Hashirama, Everybody adored Hiruzen, but villains loved Tobirama and were thankful.
