If you go to the police or FBI and offer help I am pretty sure they will say no. Except in very controlled situations they are unlikely to share any of their evidence. It is just not their culture.
However I wonder what you could achieve without their cooperation. Could you "crowdsolve" a crime? Say a website where people post what they know and any evidence they have.
In social science experiments, it's not unusual to have undergrads or grad students classify the raw data for certain characteristics (a process generally referred to as coding). If we produce (the crowd) a large amount of data, do you really think they'll reject classification information? If someone walked into their office and said "Look at this picture I took of a guy putting something in a trashcan", I suspect that person would get pretty immediate attention.
These agencies often appear to be slow because they've got political bureaucracies as well as defined processes (chain of custody in evidence is pretty important), but it's a mistake to conflate their slower speed with a lack of intelligence.
I'd be wary of people being able to submit arbitrary "evidence." The two risks that leap immediately to mind are the perpetrators offering things that direct the investigation elsewhere, and people with an agenda against $group submitting things that make it look like $group was responsible.
Not to mention that they don't want to hand out material that might be used to target wholly innocent parties. While law enforcement personnel sometimes engage in willful miscarriages of justice, this is nonetheless the exception rather than the rule.
However I wonder what you could achieve without their cooperation. Could you "crowdsolve" a crime? Say a website where people post what they know and any evidence they have.