WARNING: The following article contains spoilers from "Bloody Mary" in Are You Afraid of Darkseid? #1, on sale now.
The Mirror Master has been unique in the DCU because his ability to access the mirror dimension has thus far been unique. However, in the story "Bloody Mary" from Are You Afraid of Darkseid? #1 (by by Kenny Porter, Max Dunbar, Luis Guerrero, Becca Carey) it was revealed that he not the only being capable of moving through the mirror dimension when he encounters Bloody Mary, a villainess from Apokolips. Unfortunately, the encounter does not go well for the Flash Rogue, as Mary has dispatched him by the end of the story, potentially setting up her return in the future in Are You Afraid of Darkseid? #1 by Kenny Porter, Max Dunbar, Luis Guerrero and Becca Carey.
The Mirror Dimension is a reality that Mirror Master discovered when first experimenting with his signature weapon. If one can successfully navigate the dimension to their intended destination, then conceivably it could take them anywhere a reflection exists. It's a potentially powerful tool, but Mirror Master has thus far used it as a means of entrance and escape in his criminal career as opposed to doing anything that would make him a threat to the world.
Bloody Mary is a different story. Once Darkseid's top Female Fury, her experimental Mother Box trapped her in the mirror dimension. She has since been twisted into an abomination that feeds on blood and can be summoned by a person chanting her name while looking in a mirror. A chance encounter with Harley Quinn and Darkseid seemingly destroyed her, but in reality she was merely thrust deeper into the mirror dimension, unable to escape.
Unlike Mirror Master, Mary is unable to leave the mirror world for more than a short period of time. She is connected to the dimension by a physical tether that will pull her back in if the mirror she has come through is shattered. For all her great power she is bound to the mirror dimension with an obvious weakness to exploit should she ever breach the normal world.
Mary's encounter with Mirror Master has the potential to change her situation. More than anyone else in the universe, Mirror Master knows how the mirror dimension works. Assuming Bloody Mary doesn't kill him, she could exploit his knowledge to her benefit and force him to help her escape her prison for good.
This could have massive repercussions for the overall DCU. Bloody Mary has only made a brief appearance, but in that time she has demonstrated that she is as powerful as Darkseid. It is very possible that she is even more powerful than the tyrannical ruler of Apokolips, considering that she in all probability would have killed him if not for the intervention of Harley Quinn.
Bloody Mary's escaping from the mirror dimension would be a major threat to the peaceful existence of the DC Universe. Bloody Mary could literally go anywhere a reflection exists, and Darkseid was confident enough in her skills to believe that she could kill Orion. That kind of power set loose on the universe would be a catastrophe, and while Darkseid and his kingdom would undoubtedly be her first target, her hunger would ensure that it wouldn't be her last.