1. Unarmed mediation and intervention teams

The purposefully mentioned former violent criminals taking part in such programs. This is one thing they should've linked or provided a citation. Aside from that, the idea of breaking off the responsibilities of the police to another group is ok but ultimately pointless. They are just police with a different name.
When it comes to violent crimes in progress someone needs to be trained to deal with it. That's why even in countries where the police aren't armed by default they have the option to arm themselves if the situation warrants it. There isn't anything inherently wrong using the UK model of the police force but they still would be police.
2. The decriminalization of almost every crime

Actually there is a problem with how many laws exist we currently live in a society where everyone is a lawbreaker without even knowing about it. It would be nice to detangle the cluttered mess in our law books. The biggest barrier to this type of change though is that local governments use laws to help fund themselves. People usually aren't outraged enough over the various ticketing systems to see this trend being reversed.
3. Restorative Justice

This would be cool. The only problem I see is that it requires more diligence and participation from citizens. Considering how inept we collectively are at local politics this is a very difficult problem.
4. Direct democracy at the community level

This has the same problem as #3 but I feel it would be less effective with urban areas.
5. Community patrols 

This requires too much diligence and cooperation from the people. There are only a handful of people within every neighborhood who would have the motivation to keep this going. It really isn't much of a community project if the responsibilities are upheld by a specific minority in the social group.
This whole idea needs a rethink when it comes to scaling this among urban communities.
6. Here's a crazy one: mental health care

Yeah a lot of people have been advocating this before the article. There isn't much to be worried about with this one aside from the knuckleheads on this forum and in real life who don't give a damn about mental issues.