It looks like the dependencies for the MQTT binding (org.openhab.io.transport.mqtt) are missing.
Also it looks like you have the MQTT actions installed. I’ve read somewhere that this can cause problems.
Log into karaf and do a bundle:list to see which bindings regarding MQTT are active:
201 | Active | 80 | 1.10.0.201703020211 | openHAB MQTT Binding
208 | Active | 80 | 1.10.0.201703020211 | openHAB MQTT Transport Bundle
Those two are active in my system and MQTT is working fine 
I highly recommend to take a look at
especially
Replacement of mapdb by jsondb and
New folder structure
Those were breaking changes and you may end up in a new and fresh install …