Do I need special hardware to capture Wifi Direct traffic (not targeted to my computer) with Wireshark in monitor mode? Can I use any arbitrary wifi device with a device driver that is capable of switching to monitor mode and which supports 2.4GHz and 5GHz frequencies?
You need WiFi NICs that support monitor mode. And it requires the support from both S/W and H/W.
It is probably not a specifically made, expensive NIC card, but in the sense that it has to provide support of monitor mode from both S/W and H/W.
So the answer to the 'arbitrary' you asked is no. The monitor mode does not come with every NIC's driver.
For example, you may check the following URL:
http://www.howtogeek.com/forum/topic/set-monitor-operating-mode-for-wireless-lan-card-in-linuxubuntu