... what features would you be interested in it having?

Pre ordering, chatting, posting to the forum and definitely the function that informs you when something you want to pre order has been opened or an item you want is on special (an alarm or notification)

Anonymous smack talking

Setting up some game sessions online with other Nexus peeps (almost like what PSNProfiles does will sessions for trophy grinding - I feel that some times you play with such Rando's that you leave and don't want to add them again for a next play but maybe a group of Nexus peeps (at least we know we all have The Nexus in common)
User Review on a game like a User score/critic score
How about a game list thing where one can add a game and platform to list so we can see what we have and where we have it so don't accidentally order something we already have... (this has happen a few times)

All good suggestions, except for Teb's, but the site loads perfectly on mobile so why would you want a separate app?

The ability to tag certain forums for notifcations (and be notified of responses to your posts immediately).

Otherwise I second Llama_Ducks picks - user reviews and a feature to find online MP/coop partners would be great (and we can just ban the dodgy ones in advance - like those that ryhme with pebulot).

Even the entire Wish list thing... Notification like Steam and others have if something in your wish list goes on sale or in stock...