Depending on what state the servers are located in and whether the crimes are prosecuted at the state or federal level then you may or may not be charged by law enforcement, especially if you removed the offending content as soon as notice was provided that there was offending content on your server(s).
Even if you where to be charged and sent to court common sense would/should prevail and MOST judges would accept that you did everything in your power to remove the offending material as soon as you became aware of it being on your servers.
This comes into play quite often when web hosting companies are advised there is child pornography on their servers, which no company wants to be told is on their servers.
As long as the files are removed and any reasonable requests from law enforcement regarding account information and access logs are provided then generally you wont have any issues.
Please note this is a general statement and there are always chances that you will get a police officer or judge which will want to make an example of you, but this is where appeals work.