Imperial Officer's Helmet - on a table near the forge (this is only possible by either winning the Battle for Whiterun on the Imperial side or killing all the bandits and then returning to see the soldiers have returned.
There are multiple entrances to the fort, including a drainpipe covered with a round wooden hatch at the rear of the fort - this is especially useful for stealth. Other entrances can be doors or ladders.
There is more loot to take than just one trip, and as much again after the fort is garrisoned by Imperial troops. But because the fort will be repopulated anything stashed in the fort will be lost. So it is best to store or stash loot outside of the fort and to come back and get it later.
The dead bandit in a cage hanging above the fort is a permanent corpse.
After clearing the fort it is repopulated by the Imperial Soldiers a few days later, with at least ten soldiers patrolling the fort's courtyard, and more inside even if the player is not doing the Civil War questline. They will have rearranged part of the interior to form a barracks, with rows of beds etc. Also, the hunter's body in the Prison will be replaced by that of a Stormcloak Soldier. Once garrisoned, life within the fort does not appear to run smoothly: a couple of notes found in the chapel/lecture hall indicate friction between Agnis and the soldiers with regard to tidiness etc, and a notice pinned to the courtyard wall relates to a friendly fire accident.
If Whiterun is seized for the Stormcloaks, the fort will be occupied by Stormcloak soldiers, regardless of whether or not it was cleared out.
Outside, near the forge, there may be a horse that the Dragonborn may take without it being considered stealing.
Luring nearby giants and mammoths here is a great strategy for killing them and getting loot from Imperial Soldiers without having to directly kill them.
PC It is possible for a bug to occur that makes it so the Dragonborn cannot sleep or wait inside the buildings of Fort Greymoor, while getting the message "You may not sleep (or) wait while being asked to leave." The guards do not become hostile or defensive and act as they always would. Nobody will ask the player the leave. The player may still wait outside. As of the moment, no fix has been found for this (unconfirmed) as leaving the Fort and returning will not correct the problem. Loading a previous save BEFORE the message started appearing may (unconfirmed) fix the problem.
PC 360 PS3 Agnis may glitch in her bed, appearing to be sleeping but still being able to talk to the player normally. When she runs out of dialogue, she will get out of her bed and then promptly return to it, resetting all of her lines. She will not respond with her normal lines when talked to in this "resetting" phase, only offering the randomized "Hmm?" and "What do you need?" phrases.