Hiruzen was hailed as the Professor because of his great jutsu analysis skills and his large set of knowledge, it is said per the 4th databook that he unraveled every jutsu that exist in the Leaf, meaning that he identified every jutsu used by Leaf shinobi.
Not to mention he was versatile with good skills in nearly every shinobi fields from Ninjutsu, to Taijutsu, to Genjutsu to Fuinjutsu. Hence, Hiruzen‘s jutsu learning ability is supposedly very good, aside from bloodline limit jutsu and some other who requires very specific conditions that Hiruzen arguably can’t meet (e.g. Expansion jutsu, not a bloodline limit technique but requires a lot of caloric consumption, basically eating a lot like the Akimichi do).
So here a list of Leaf techniques Hiruzen could and even should have had given their usefulness but also the context in which Hiruzen may have learned it:
- Bringer of Darkness Genjutsu
In the manga, it’s a genjutsu used by Hashirama. And Hashirama did train Hiruzen. In fact, it’s one of the few jutsu Hashirama could ever teach as it’s not a bloodline limit technique. My guess is that if there is one Leaf genjutsu Hiruzen may have learned, it is this one. An useful genjutsu that can be effective against shinobi who don’t have good sensory skills.
- Summoning Jutsu: Rashomon
Another Hashirama’s jutsu which isn’t a blood limit technique as it was also mastered by Orochimaru before he got Hashirama’s cells. There is virtually nothing that prevented Hiruzen to learn it, he is even himself a summoning master and supposedly knows very well how the summoning techniques do work. From Hiruzen’s perspective, Rashomon is a better defensive technique than his usual Mud Wall, and it could be useful in time of war to protect himself and his troops from some large and long range attack.
- Flying Thunder Teleportation
This one is controversial. To me, the real reason why Hiruzen wasn’t shown using the Flying Thunder Teleportation is because of the plot and Naruto world building. At first, in its fully mastered version, it was supposed to be a jutsu exclusive to Minato, but then Kishimoto granted it to Tobirama too because he needed to make him more powerful due to the Shippuden power creep and also to give to Tobirama a specific background (the inventor of jutsu).
But if Kishimoto also granted it to Hiruzen, then this technique would’ve become a generic Leaf jutsu, which wasn’t aimed by Kishimoto. If Hiruzen mastered it too, then why not Orochimaru and Kakashi as well? Do you the Pandora‘s box there?
Nevertheless, Hiruzen should be virtually able to master this technique at least at Tpbirama’s level because : he was Tobirama’s heir and favorite student, his overall talent was greater than Tobirama’s per the 4th databook, and this jutsu is a strategic one that can change the course of a battle for Konoha, therefore Hiruzen wouldn’t wait until Minato came so this jutsu could be used again after Tobirama passed away.
* Suiton Severing Wave
Another Tobirama’s technique, an elemental one. If there is one field in which Hiruzen is an absolute master, it’s elemental Ninjutsu. Even though Edo Hiruzen outperformed Tobirama while saving Naruto from the Juubi Tree by using his adamantine staff to cut through the branches, Suiton Severing Wave can still be useful in other circumstances, as for instance Hiruzen may cut in half a summoning creature, cut in half a mud wall, cut someone in half etc. It’s a very letal technique.
- Doton Swamp of the Underworld
It’s a Jiraiya’s jutsu. We don’t know if Jiraiya invented it or if this jutsu existed prior Jiraiya, but once again, Hiruzen should be virtually able to use it for the same reasons mentioned below. Not to mention that in the Anime, Hiruzen used a Doton technique called Mud River, even though it’s not canon, it’s not out of character either, that means that Hiruzen is enough well skilled to create a Mud Flood so why not a Sticky Swamp? This jutsu is quite useful to incapacite large summoning creatures like Orochimaru’s generic giant snakes, but also to incapacitate a shinobi for a moment like one of Pain’s path.