Fellow Peterborough resident and commuter here!
All lifts are operational (or have been unless there has been a fault that has developed with them that has prevented there use today - I have been working from home today!)
Platform 2/3 waiting shelter won't be opened till Mid Jan.
Frieghliner are in dispute over their replacement mess/SOP facilities (the building at the south end of platform 6/7.
Arrangements for train dispatch don't seem to have been altered so staff are now running between platforms more than ever, this seems to almost defeat the point of putting the new platforms in!
The project is far from finished, the "finish" of the station at the moment is appalling, hoardings and exposed cables and wiring all over on the footbridge. No clear join between the old and new portions of the footbridge roof. I haven't used the parcels bridge yet.
There is also the matter of the west end entrance to the station which has not been constructed yet, not sure what is happening with this. Given the hoardings at that end of the footbridge I assume this is still continuing.
Operationally, the project has been great, and is a big boost to a critical junction, but if you look at the rebuild and remodelling of other stations - it is appalling when it comes to the customer facing element.
Just to address a few points from other posters:
First Class lounges have been looked into many times by EC, NXEC and GNER, its not commercially viable. The first class season ticket holders who commute from Peterborough do not spend enough time at the station, as a first class pass holder myself, I can confirm most first class passengers on the 0610, 0640 and 0700 all turn up a few minutes before and get straight on.
The amount of business travel down to London with First Class tickets again does not justify the costs, which would be substantial when you consider that the lounge would probably need to replace one of the existing station tenants, and there is a sizeable income lost.
And regarding platform 2 being used on Sunday for XC, platforms 4-7 were under possession at the time.