I decided to start a new save and forgo the new expedition feature in the Anomaly. I feel like part of the fun is starting from scratch and finding shortcuts to get units, complete milestones, etc. Plus I often play my expedition saves even after the expedition is over.
I made it to Phase 3 before I quit playing today. Overall I like the expedition. Nothing has been particularly annoying but I guess that could change in the next phases.
It looks like the expedition is finally over since the last optional milestone was reached; however when I go to collect the rewards and officially end the expedition, the game locks up. My character just stands there and the controls have no effect. Hopefully they get that fixed soon.