Abilities and Powers
It is stated that Jinbei was able to battle Portgas D. Ace as his equal. They both nearly killed each other in a five-day long fight just before Ace was taken in by Whitebeard. It is unknown if they're still equal in power. This means he has the ability to damage Logia Fruit users, though if this ability stems from Haki or another power is unknown. In Impel Down, he shared the same cell as Ace, who was considered one of the most important prisoners in the world at that moment. Otherwise, Jinbei and Arlong were once said to be equals, though whether it regards to their strength or status is yet unknown.
Being a fishman, Jinbei possesses super-strength. In fact, he is stronger than all the rest of fishmen seen until the moment. He also appears to be quite swift, even on dry land, in contrast to his large size. He could intercept an enraged Luffy (in Gear Second mode) and prevent him from further assaulting Blackbeard.
Though strong, he admitted himself that he is of no use on land battles, implying he is much stronger at sea. In Chapter 546, Jinbei stands up to this claim when he lifted one of Impel Down's massive entrance doors and used it as a raft to provide passage over the sea for Crocodile, Mr. 1, and Buggy (all Devil Fruit users), with himself acting as the raft's propeller underneath. He not only managed to pursue the fleeing battleships, but even outmaneuvered the incoming cannonballs fired at them by the Marines with relative ease, all the while bypassing the Sea Kings that infested the surrounding waters of the Calm Belt.
From his demonstration of underwater activity, it is obvious that he does not have the powers of a Devil Fruit, even at one point cursing the weakness of Devil Fruit users as he saved them from drowning. His power over sea water may very well make Jinbei a natural enemy of all Devil Fruit users, as seen against his fight against Gecko Moria in Marineford, where the fishman rendered Moria's ability to summon his zombies useless by splashing them with sea water. As a fishman who is familiar with the sea as much as the back of his hand, he is a capable helmsman, shown when he steered the stolen Marines battleship.
Also, Jinbei has a huge tolerance for pain: not only he was one of the few people to be able to take a "baptizing" in boiling water in Impel Down without flinching, which is considered an impressive feat, but he could stop a direct magma punch from Akainu with his bare hands, unperturbed despite being burned.
Jinbei also has a knack for discerning enemy military strategies after witnessing any subtle change in enemy formations, as seen when he quickly guessed that Magellan dispatched the order to the battleships outside the Great Gaol to flee during the Impel Down mass breakout, and during the battle in Marineford where he surmises that that the Marines were plotting something after Ivankov informs him the the enemy is retreating further into the plaza.
Fishman Karate
Jinbei is a master of Fishman Karate, which he can use to knock away many guards at once. His strikes are so strong that he doesn't even need to make physical contact with an enemy as the very air will blow them away. Another example of his strength and Fishman Karate level is that he defeated Minorhinoceros, one of the four Demon Guards, with a single uppercut, while Luffy used his Gear Third to defeat another Demon Guard.
He also displays being able to manipulate water as if it were a tangible cloth through Fishman Karate and Fishman Jujitsu, even using it to attack from a distance. He can cause devastating damages with this kind of techniques, both to people and ships.
Thanks to his mastery on Fishman Karate, Jinbei can perform blocking moves which are able to stop attacks as powerful as the thrusts from a shadow-strengthened Gecko Moria, a member of the Shichibukai.
Interaction With Fishes
Jinbei has shown the ability to communicate with fishes, even at a long distance. He summoned a large school of whale sharks to the Calm Belt (which was usually too dangerous, with the Sea Kings infesting it) to assist him in a mass-breakout of Impel Down. He can give the whale sharks precise orders, so they understand and obey him. The ability to speak with fish is usually unique to merfolks, so Jinbei's capability to do so is considered noteworthy by Crocodile.