This won't cover things like agility, speed, being able to take apart bombs, etc. This will mainly have to do with abilities that seem unusual or what languages he knows. The latter will be added just because it'd be amusing to keep track of it.
(Pre-Flashpoint) Red Hood Lost Days showed Jason knew German, Russian (though he claimed it was limited *1), and could also read lips.
In Death in the Family Jason spoke Arabic something that he was shown knowing in DCnU in RHATO #21.
Sees things others can't: Jason has been shown seeing Essence when no one else can and talking to Ducras' ghost. (*2) Essence did appear to others once she was wounded and got into a heated argument with Jason. The extent of this ability hasn't been tested. It could be something he gained during his training or a side effect of returning from the dead. Perhaps he can only see members of the Untitled.
Can control his body temperature: This was done somewhat subtly in RHATO #5. The trio all fall into icy water during the issue. Kori of course isn't affected once her powers come back. Roy is shown shivering and speaks through a chattering speech. Jason isn't affected at all and fights back like nothing happened.
Can hold his breath for long periods: Hinted at in the same issue since his last test as part of "the cleansing" was underwater. In present day the Untitled he was fighting assumed he had drowned because he had been under so long.
Fight Blind: During the crossover with Teen Titans during DOTF it's noted by Tim that Jason can fight with no difficultities when he can't see.
Unaffected by paralyzing toxins: RHATO #15 had Joker inject him with such a toxin but Jason mentally comments that thanks to the hellish training he received from the All Caste they don't work on him anymore. Curiously Cheshire planned on using such a toxin on Jason in the annual. She never had a chance to do so but it shouldn't have affected him anyway.
Awareness of his body: Given the examples above this seems obvious in hindsight as he has more control over his body than most. In RHATO #36 Jason says that since he returned from the dead he's very aware of any change to his body. While under the influence of venom he could tell how it brought up his heart rate despite being affected by the drug. This also explains why Jason was aware he was in a coma in RHATO #18. Strangely he was also aware of what Alfred and Bruce were saying while he was in his coma.
Able to Resist Mind Control: The H.I.V.E. Regal tried to enter Jasons' mind but was unable to thanks to the training he received from Ducra in RHA #10. (*3) Underbelly also tried to control Jason but couldn't because he wasn't actually evil. Jason wasn't however able to stop himself from being drawn in to a fantasy Chrtimas world in RHATO Annual #2. He was able to snap himself out of it.
*1 He seemed to speak it well before he made that claim. Amusing enough Tim Drake had problems with his Russian in Red Robin.
*2 It wasn't shown if Roy or Kori could see Ducra or even heard what Jason said to her. Tynion has S'aru and Essence being able to communicate with Ducra although both have supernatural powers.
*3 Like most of these examples it was shown in Jasons' solo series which likely means most writers won't bother to research these things to see what he can do.