First off i would like to say i love Debian greatly. I love apt as well. 15,000+ packages is simply amazing and its the main reason why I used Debian. I would like to suggest some very simple features that i feel would greatly improve apt.
When you are setting up a new system you have to install a number of new pieces of software. It would be nice if you could run more than once instance of apt. It would also be nice if I could connect to a number of mirrors and download from multiple sources. Maybe running a trace route to all of the apt mirrors at install and using the top 5 or whatever closest mirrors. Splitting up a file into multiple peaces would be nifty, but it would add a greater level of complexity. As would a p2p model like BitTorrent, which I would most defiantly donate my spare bandwidth to apt. I think if there is multiple files to be downloaded then it should only download one file from one mirror or something to that effect, possibly going down the list of mirrors that is sorted by distance from the computer. I am not sure how synchronized the apt mirrors are, but I assume a number of them are pretty stable. This would speed up the update and download process as well as spread the bandwidth between the mirrors more evenly. I am not sure if I download a whole new package list every time I do a apt-get update. But it would be nice if I notified the mirror when I last updated and then the server only responds with the new listings. This would save a few seconds and a few k, but though seconds and k add up. I am not sure that everyone knows about apt-get clean, maybe an automated system that runs apt-get clean periodically would be in order. Thank you for very much Debian and apt, i use it every day, and i am not sure what i would do with out it. peace