As part of the master plan for finishing the Saint Paul Grand Round, a path has been built next to Wheelock Parkway between Rice and Westminster. It is beautiful (photo at right). Wheelock remains closed between Westminster and Edgerton, as they're putting in actual trail access from Wheelock to the Gateway Trail (as opposed to the erosion-causing unofficial access that's existed for the past few decades).
On the subject of the Gateway Trail, it's still closed south of Arlington. It seems MnDOT is behind schedule. Contact me if you know whether they've put through the connection to the Trout Brook Nature Sanctuary at the southern end (I'm guessing no).
Finally, the Lexington spur of the Lake Como Trail is closed at Como Avenue, but can easily be bypassed by riding on the sidewalk on the other side of Lexington (or on Lexington itself).
UPDATES: Wheelock Trail coming along nicely, Gateway Trail remains closed through Arlington, Como spur trail closure