X11 (the video display technology in Linux systems like LTSP) was designed to be network transparent.
Cons
Keep in mind three things:
Each situation may not apply to your business or organization.
There may be workarounds.
LTSP is improving.
Reliability
Terminals are always dependent on the reliability of the network infrastructure. (In my personal tests, the terminals gracefully survive short outages. Also, our cheap, scattered network works reliably except in power outages.)
The terminal server (and whatever servers provide support services such as DHCP and TFTP) may be a single point of failure unless a cluster or failover system is setup. (Did you buy high-quality hardware and get a good warranty?)
A few applications do not support ESounD, so the audio may not work.
ESounD under LTSP does not support software mixer volume control.
Performance
A terminal setup may not be appropriate for certain work cases (e.g. video editing, high-end games, Google Earth) that tax the network or server hardware.