It is becoming more and more common for the legal system to rely on IP addresses as a basis for identifying criminal activity. Is there a better way?
http://www.nytimes.com/2014/05/22/nyregion/dozens-arrested-in-new-york-state-child-pornography-investigation.html
No. It might be becoming more common but an IP address does not identify a person. You need to search a suspect's possessions before you can have any evidence. It might be reasonable for the police to use this lead to obtain a physical address then search for CP but an IP address along should not be sufficient.
Thankfully courts are beginning to realise this fact in regards to copyright infringement. [1]
An IP address (which is matched to a specific "customer" MAC address or login name. ISPs do log this stuff.) is enough for probable cause and a search warrant. The law enforcement agency then executes a search warrant and finds evidence, and the case is further built off of this. If the case goes to trial, the IP address is a mere stepping stone in the prosecution's case, and not much more.
Thankfully courts are beginning to realise this fact in regards to copyright infringement. [1]
[1] https://www.techdirt.com/articles/20140122/07375025953/court...