To repeat a suggestion to expand on this list, I think it would be hugely helpful if the giveaways (and trades, for that matter) could be listed by product, rather than by drawing. It could reduce the number of pages that you have to wade through tenfold or better and make it easier to focus on...
I think making the person's Steam account visible would make a significant difference, simple to implement, and with precedent (this is how it's done on the Steamgifts site that IG copied for its Giveaways).
Currently, I don't see anything preventing someone from using your Steam name and...
This may have been suggested before, but I would like to recommend that the Giveaways section fo the site be organized so that each game has one page, rather than one page per drawing. For example, I can ignore the one page dedicated to Savage Resurrection instead of loading page after page...