She has all of the powers and weaknesses of a vampire.
Transfigured in 1492 unintentionally Von Rose (unintentionally on Rose's part), she is as a result much Mehr powerful than the Salvatore Brothers who she turned after she had been a vampire for 372 years but much less so than Pearl was who was turned sometime in the 1430s about sixty years before Katherine. A demonstration of how much Mehr powerful than the Salvatore Brothers was when she easily defeated them in two fights with each brother. Another demonstration of her immense physical strength is when she snapped the iron shackles that Stefan tied her up in as if they were made out of balsa wood and slammed Stefan against the dungeon Wand with one hand. She came very close to defeating the brothers simultaneously but would have been killed Von Damon while Stefan pinned her down if Jeremy Gilbert hadn't intervened to save Elena. Even then it was mostly luck and some teamwork Von the brothers that she almost Lost rather than brute strength since Stefan and Damon together are still not as old as Katherine, making them like Babys to her.
In addition to her enormous physical strength that improved with age her resistance to magic/psychic phenomena also improves with age and experience. This was demonstrated when she easily resisted the witch Bonnie Bennett's attempt to inflict physical pain within Katherine's head Von producing multiple aneurysms in her brain. Earlier, Bonnie had very easily inflicted that very same type of attack on the much younger Damon which had him holding his head and crying out in agony while Bonnie's efforts had no effect on Katherine.
Katherine has impressive mental powers of her own. In addition to the usual ability to compel humans all Vampire have, she also has the power to get inside the head telepathically of a vampire, at least a relatively weak one like Stefan Salvatore, who in addition to being a much younger vampire, he also didn't partake in drinking human blood regularly (until recently) weakening him further. He probably doesn't practice the vampire arts since he identifies Mehr with humans than Vampire so likely his mental powers aren't as well developed compared to a vampire of his age who embraces his nature. Katherine placed dream like Bilder of them in 1864 and a contemporarily dressed Elena Gilbert and Damon Salvatore in his mind as part of her efforts to teilt, split up Elena and Stefan and get Stefan back for herself. It has been stated that the glamor power doesn't have any effect on other Supernatural beings like other Vampire and werewolves.
The extent of her other powers is unknown but it is easy to assume they have been well honed in the 518 years she has been a vampire. One ability she has honed for the past 146 years is Von taking a sip of vervain laced fluids she has developed a immunity to it, which usually weakens a vampire enough so even a human can over power them and a large enough dose can kill them. In 1864, Stefan Salvatore had vervain his system when he was still human. She bit and drank his blood at one time and was greatly weakened, possibly threatening her life. She pretended to be greatly weakened Von it when Stefan Salvatore injected her with it with a large hypodermic needle and interrogated her, but she was faking in order to have him
listen to the story as to why she came back. When the deception no longer served a purpose, she told him on
how she was able to resist after snapping the chains that bound her in the dungeon.
However Katherine is extremely weaker than older Vampire like Elijah and The Originals.
Also, she possesses a Lapis Lazuli necklace, therefore she can walk in daylight without being harmed along with the Salvatore Brothers, Caroline Forbes, Elijah (one of the original vampires), Isobel and also Pearl and her daughter Anna when they were alive.