Is this meant to be a mobile device?

Obviously a small power consumption and size leads to the idea that it
is for mobile usage. I can easily see mini blue tooth keyboards being
use with this but what about a display? What kind of display is
intended to be used with this? TVs? Monitors? Those aren't mobile
displays. It is also mentioned that you could run this thing on solar
power which further suggests a mobile intention.

Is there going to be an easy way to connect small TFT displays to it?

If it is not meant as a mobile device (which disappoints me) I can see
other application for it such as thin clients and media streaming
devices or file servers.

The BeagleBoard is meant for many applications where low power and high performance running a high level OS is required. As it does not come with a battery, it isn’t portable ready. I suggest you read the Reference Manual to understand what it has on it. It can most certainly be used in a mobile application, but low power is not a mobile only domain. OMAP was design for use in Cellphones and mobile devcies, such as the Nokia N800 and the Archos 5, so mobile is definitely something it can handle.

It supports S-Video and DVI-D. DVI-D to LCD adapters are out there today to help you connect it to a LCD display. Future versions of Beagle could in the future have support for an external LCD panel.