Can I be denied to move into a rental home if....?

The last place, before the one I am at now ended up getting bleach on the rug. I do not know how because the only bleach I had in the house was some wipes and some bathroom cleaner that never was even in the living room. I was told by my mom that when she was in there that the lady who came into clean out the unit accidentally spilled bleach, but again I am not sure since I wasn't there. Not only that but my bathroom mat bled on the bathroom floor a stain that was roughly 2 inches in diameter (blue). Otherwise the two places I have lived in have been taken really good care of, minus children's feet running across carpeting, which will be professionally cleaned when I leave here. I am just worried that the application I fill out will be denied because my old landlord took me to court. She had pictures so therefore she won her $400 for replacing the carpeting in the lliving roomand the little patch of tile in the bathroom, that was paid off. I just basically worry because I need to get out of the small town I am living in and go back to Chicago to find a job, since the town I live in, in MN lacks them.