If I have the steam client open on one monitor and the chat window in another monitor and try to drag an item from my inventory and drop it to the chat to make an item shortcut, it does not do anything. If I move the chat window to the same monitor as the steam client, dragging an item creates and posts a shortcut as expected. If I place the chat and/or the steam client window to be on the both monitors at the same time (i.e. place the window on the point where monitor areas meet, so a part of the window protrudes to another monitor), than drag&drop works fine, too.
Since this works on the Windows client on Wine and, IIRC on the Windows client natively on Windows, I consider this a bug in the Linux client.
I have one large X screen spanning across two monitors.

My system information:

Processor Information:
    Vendor:  AuthenticAMD
    CPU Family:  0x15
    CPU Model:  0x2
    CPU Stepping:  0x0
    CPU Type:  0x0
    Speed:  3700 Mhz
    8 logical processors
    8 physical processors
    HyperThreading:  Unsupported
    FCMOV:  Supported
    SSE2:  Supported
    SSE3:  Supported
    SSSE3:  Supported
    SSE4a:  Supported
    SSE41:  Supported
    SSE42:  Supported

Network Information:
    Network Speed:  

Operating System Version:
    Linux Mint 16 Petra (64 bit)
    Kernel Name:  Linux
    Kernel Version:  3.11.0-17-lowlatency
    X Server Vendor:  The X.Org Foundation
    X Server Release:  11405000
    X Window Manager:  Marco
    Steam Runtime Version:  steam-runtime-release_2014-02-05

Video Card:
    Driver:  NVIDIA Corporation GeForce GTX 770/PCIe/SSE2

    Driver Version:  4.4.0 NVIDIA 334.21
    OpenGL Version: 4.4
    Desktop Color Depth: 24 bits per pixel
    Monitor Refresh Rate: 119 Hz
    VendorID:  0x10de
    DeviceID:  0x1184
    Number of Monitors:  2
    Number of Logical Video Cards:  1
    Primary Display Resolution:  1920 x 1080
    Desktop Resolution: 3840 x 1080
    Primary Display Size: 23.54" x 13.23"  (26.97" diag)
                                            59.8cm x 33.6cm  (68.5cm diag)
    Primary Bus: PCI Express 16x
    Primary VRAM: 2048 MB
    Supported MSAA Modes:  2x 4x 8x 16x 

Sound card:
    Audio device: Realtek ALC898

Memory:
    RAM:  7883 Mb

Miscellaneous:
    UI Language:  English
    LANG:  en_US.UTF-8
    Microphone:  Not set
    Total Hard Disk Space Available:  398075 Mb
    Largest Free Hard Disk Block:  133512 Mb

Installed software:

Recent Failure Reports:
    Sun Mar  9 13:51:51 2014 GMT: file ''/tmp/dumps/crash_20140309155125_29.dmp'', upload yes: ''CrashID=bp-817e2af1-6f5d-48c8-a807-ed1ae2140309''
    Mon Mar 10 16:37:20 2014 GMT: file ''/tmp/dumps/crash_20140310183710_46.dmp'', upload yes: ''CrashID=bp-7a02df35-022f-4c03-8719-37e272140310''
    Thu Mar 13 17:55:44 2014 GMT: file ''/tmp/dumps/crash_20140313122157_1.dmp'', upload no: ''Failure when receiving data from the peer''