In general, if you allow anyone to be a router then anyone can advertise a low-cost route to anywhere, and then drop the packets. You might be able to combat that with some kind of decentralizes reputation system or policies that prefer existing routes that have been in use for awhile and are known to work, or that sends a few test packets over any new "suspicious" link before using it send real data.
I don't know what current research says about this problem, or whether any current routing protocols attempt to deal with it at all.
In practice, I expect that real wireless meshes can still be somewhat secure by operating as managed clusters of routers that don't peer with other clusters of routers without the administrator explicitly enabling peering. So for instance, you might have one neighborhood with a dozen houses with routers managed by some guy, and a nearby HOA with another cluster of routers managed by someone else, and they might find out about each others' networks and agree to create a bigger network by peering. So, your network's trust model can piggyback on the trust model of the real world -- if you know someone in real life, it's a lot less likely they're going to try to take down your network than some random person you don't know.
I don't know what current research says about this problem, or whether any current routing protocols attempt to deal with it at all.
In practice, I expect that real wireless meshes can still be somewhat secure by operating as managed clusters of routers that don't peer with other clusters of routers without the administrator explicitly enabling peering. So for instance, you might have one neighborhood with a dozen houses with routers managed by some guy, and a nearby HOA with another cluster of routers managed by someone else, and they might find out about each others' networks and agree to create a bigger network by peering. So, your network's trust model can piggyback on the trust model of the real world -- if you know someone in real life, it's a lot less likely they're going to try to take down your network than some random person you don't know.