Properly installed and maintained K&T is quite safe, though it would
be a good idea to install GFCI outlets (properly labeled "no
equipment ground").

The problem comes if it either wasn't a great installation in the
first place, or if it's been tampered with or damaged.

A good solder joint will last a century or longer, but a bad one can
get worse over time, e.g. corrosion from leftover flux, a cold joint
developing increasing resistance, etc. Depending on the age of the
house, the wiring may have been soldered using irons heated over a
fire, which made cold joints more likely since the iron didn't
maintain a constant temperature.

Many times you'll find amateurish additions to K&T systems, I've seen
Romex twisted on and wrapped in duct tape for added lights or
outlets.

Some homeowners have blown insulation over wiring that was fine in
open air, but gets too hot without air circulation.

My own house was almost entirely K&T when we bought it, mostly on one
breaker (and a Zinsco breaker at that), so the insurance inspection
was more detailed than usual, and the inspector asked about what
appliances were going to be used in which rooms so he could get a
better idea of whether the wiring would be safe as we were using it.
No trouble once it was inspected and approved, but not every
insurance company will accept K&T.

--
is Joshua Putnam
http://www.phred.org/~josh/
Braze your own bicycle frames. See
http://www.phred.org/~josh/build/build.html