Personally the way i would want things is:
Monument of Honor:
No changes to this as such, but a rather large addition. I would like to see, instead of a weird watery wall in the background, a tapestry of your own character. You would simply wear the armor/wield the weapons you wanted on display and then pick a pose from a list. No limitations on whole armor sets being worn, you could mix and match what you liked. In my opinion this would make the HoM feel far more personal and add a nice feel of nostalgia when we first start GW2.
Monument of Fellowship:
The obvious change i would have here would be for each statue to display the armor your hero has been upgraded with in order to allow you to display them - i worked hard to upgrade Razahs armor, and the artwork implemented by the Devs is fantastic - why not show it off?
Also the ability to choose each individual hero you want to display as opposed to a random shuffle button (that never gives the outcome i desire)
Monument of Devotion:
It really is a shame to see a Baby moa standing still staring into space when his animations are so detailed and imaginative. I would like to see all the minipets on display moving about as they do in an outpost. Imagine a full set of minipets on display strolling about.
Monument of Valor:
Well, i would like to be able to choose which weapons are on display, but i can see why its the way it is, so i'll leave this one be
Monument of Resilience:
Instead of having your armor displayed on your characters model, i think it would look far more professional to have a sort of 'armor stand' on which the armor you wish to display is worn. This way several could be displayed without clones of your character all over the place ruining the feel.