I have the same issue. My fiance has the same issue, albeit she is running Windows 7. Seems it's not just a Linux issue.
Issue was fixed in last client update.
Can confirm - there was a beta client update that fixed this across all platforms, closing :)
Hello John
Just writing in to tell you that the issue is still not fix. We're both able to put items now on the trading box without the message "Waiting for other player", but even though I can do that, the window still refreshes.
If we're fast enough to tick that we're both ready and click on the mark exchange box, nothing happens. The window refreshes, the item picture won't show and is just a spinning circle.
The only thing that has been fixed here on our side, is that the item server sees us both as wanting to trade, not just the one of us. Other then that, window still refreshes every 3 seconds and we're unable to trade. I'm also unable to give her something in return. I try the drag & drop method but it will not go int the trade window. It just refreshes the page. The issue still persists, sorry.
Edit: Tonight we tried again, as it did not work earlier even after the steam update and it started working again.
Nothing extracted yet.
[Arch linux amd64]
As of today's update (120314), trades can no longer be completed. The trade window opens, but if you try to send a chat message the entire page visibly refreshes (as if you hit F5) and nothing is sent. Likewise if you try to add an item or change item page, so you can never populate your array of offered items. Sometimes it won't even list your inventory items at all.
If the other part adds an item it shows up in his offerings without an icon (just the spinning throbber), and the chat says 'player added Unknown Item'.
This happens both if attempted ingame via the community overlay and in the Steam client proper. Nothing of any interest is output to the terminal. Persists over client restart.