Try out our new Trade Site!

-Language support
I personally have no issues with English and use an English client as well, but I'm not everyone)

-Collapsable UI
The poe.trade UI is over a screen long and I can either collapse all of it or nothing, and I rarely need to access more than 2-3 sections.

-Two Column Layout for Search
I also like this part, because it makes the whole thing more compact and fit on a widescreen monitor. Not everything on poe.trade is aligned vertically, but there's a lot of vertical scrolling involved compared to this UI (also see the point above).

-POE-Feel
Now this may not seem that important, and it really isn't when it comes to efficient trading (which is what we like), but seeing everything in sans-serif gets old and doesn't make it feel like trading is part of the game. I could live without the background, but at least the UI is considerably wider than that of the forum.

-Language Flag next to Sellers.
Though I'm not 100% sure on what they're supposed to say. For instance, do Russian players play on the same server and can I expect them to understand English? Or am I supposed to only ask English and German people (or French, but my French is really not that good anymore)? In general as above I'm glad, that language is a part of it.

-Official Portal
It's finally official. There have to be improvements made so that it can actually be used, but I'd very much prefer to trust an official site in the future than something private where I don't know what's what.

-The UI for search results
It's bad. I appreciate that you wanted to keep it as close to the game as possible, but that makes it very inconvenient to use. I don't need a popup covering half my screen with all the stats, especially if I'm searching for uniques which all have the same stats except for some variable ones or enchantments / corruption. I will elaborate on finer points that really need to be fixed apart from this, but technically speaking they're still part of the search results.

-Custom filters
You allow to search for a weighted sum, but you don't allow filtering. I've just discovered the way to look for elemental dps, but it's slightly elusive. I blame the UI. EDps can be quite important and should be listed somewhere visible, not in the bottom right corner overshadowed by the game-like tooltip. Here, my tip is to create a multi-column layout. Keep the font and such if you like, but do make the summary and custom filter calculation results available easily and compactly. poe.trade does a very good job with summarised stats of an item, but imo listing the custom filters beneath all the regular properties of the item is a mistake. I'd much rather have it next to the other calculated values.

-Affixes
This has been said a lot; it's also one of the most important features. I've had one example of this in poe.trade just now (this was actually before I discovered how to sort by eDps on this site, but then again I have been using poe.trade for a while longer).
I was looking for a wand with high eDps, willing to pay at most 50 chaos. So far, so good, I should be able to do this here as well (as I know now, anyway). Then I've noticed, that many of them already had a crafted affix, so I looked for ones without one. And surprising as that may have been, the top choices didn't have a much lower dps. After that, it was the matter of isolating the ones I could still craft. And this step is something that is utterly impossible with the current official tool. Unless you check the possible prefixes and suffixes and hybrid value allocations among these (e.g. spell damage / mana prefix for casting wands) or are experienced enough to tell with one glance, it's not feasible to check whether an item can be crafted or not.
By using poe.trade, I ended up paying exactly 50 chaos, crafted a max roll attack speed mod and ended with a cheap rare wand that is going to trump the Piscator's Vigil, that I already have.

-Completeness of filters
This is something that does not belong to the search results anymore but the search itself. While eDps may "work" for weapons, it doesn't exclude crit or attack speed. On poe.trade there is "elemental damage added to attacks" (or something similar anyway), conveniently disregarding the element dealing the damage. Here I can at most create a weighted sum, but lo and behold, it does not work. The items aren't matched properly and if they are (by entering a minimum value for the sum, which should obviously be unnecessary), I can't sort them (see above).

-Including acquisition
Your tool would have to be a major improvement over poe.trade before I consider browsing an "incomplete" database.

Unlike the previous posters, I could however not find flaws in its performance. Either people aren't using / testing the tool right now (which seems unlikely to happen during a friday evening in Europe, even if most people still prefer poe.trade), or the flaws have been dealt with / have occurred entirely client-side.

I do feel like I had some more points to mention but they appear to elude me just now. On to the next section.

Especially over poe.trade. Why restrict yourself to making an inferior version of something that exists when you can make a superior version instead!

-Item category
Unintuitive name, but I suppose it's the official one and one might as well get used to it. Can be somewhat confusing when compared to "item class" based Ancient Orb. Major problem: Very unfriendly to mouse-only users. I understand that it's natural to use the keyboard during the game (although of course one might use it with a high-end or mmo-mouse with many buttons), but unless one is actually only alt-tabbing, using only the mouse to navigate a browser doesn't seem that counter-intuitive to me. It's a lot to scroll because the division into large categories is also included in the list and it's easy to scroll past the category you're actually looking for.
My suggestion: Add larger divisions as optional dropdowns. It won't hurt the other users much if they still want to type and scroll, but I can also click through e.g. "Equipment->One-Handed-Weapon->Wand" without wasting much time.

-Do the same thing for stat filters
It will be a lot tougher to divide that into categories, but it's definitely not impossible. One example of such a division might be "Affix->Suffix->Resistance->Fire Resistance". Note that I'm not saying this kind of division is perfect, but it helps finding the exact mod you want and not using an implicit or crafted mod by accident or even a prefix instead of a suffix. One of my most important personal reasons for this is that even if I manage to find the correct mod or stat by typing it, I always have to think of the most unique substring to type with my left hand or moving over my hand from my mouse. This may sound petty, but it's an inconvenience, and if UX is important to you, it's something that can be fixed. It might be more convincing if I say that it will also be much more intuitive to players who are unfamiliar with the system instead of offering them a myriad of options in a single dropdown.

-Place custom filter calculation results next to commonly calculated stats of an item
See above. I really think that this would improve the way experienced users handle the system. It won't obstruct the view of people looking for the regular values on the item itself and it will make sifting through lots of similar items and comparing them that much faster. I know you don't want people to trade quickly, but I also hope you want people to play the game rather than looking through lists for hours.

-Provide actual information on item affixes
I'm not sure if you'd even consider to do this, and I'm guessing the current API doesn't expose this information yet. But it'd be a real bonus for people who really want to minmax their items and not buy the wrong ones. I see your point about wanting item progression to be slower and more gradual by finding your own items, but considering the mass of available item combinations, that's not realistically possible either way. And even so, forcing people to be frustrated with failed and gambled purchases of items that may or may not have the required (open) affixes can't be your concept of coming closer to that ideal.