Confusion; Distraction
Aircraft Equipment Problem Less Severe
Flight Crew Landed in Emergency Condition
Aircraft
Upon liftoff; nose gear had unusual amount of vibration/wobbling; however; gear retracted normally.  Upon selecting gear DOWN; nose gear slammed down with green indications. Requested flyby of ZZZ1 tower which reported gear did NOT appear to be all the way down.  Additionally; [another aircraft] reported that nose gear appeared 'cocked.'Returned to ZZZ1 with uneventful landing.Taxied clear of runway.  Inspection by Crash Fire and Rescue (CFR) and ZZZ1 maintenance reported no damage.  Gear pins were installed by ZZZ1 Maintenance on taxiway and proceeded to gate with no additional events.Entry requesting inspection of nose gear made in [logbook].
Upon the fly-by; the Tower said that the NOSE gear seemed to be extended abnormally. I flew the go-around; while the Captain received input from an [aircraft] on the ground; who observed our flyby as well. That flight also reported to the Captain that the nose gear appeared to be extended abnormal. We checked the QRH; and then we returned to land and landed uneventfully.
A B767 flight crew noted an unusual vibration upon gear retraction. They continued to their destination and when they selected gear down the nose gear seemed to immediately fall into place. They did a Tower fly-by and both ATC and another pilot observing said the gear appeared to be extended abnormally. They continued to land without incident.