What is the longest observable wavelength of light using an optical telescope?

It depends on the telescope.

If the telescope is fully reflective (no transparent glass elements), it should be able to operate well-beyond visual wavelengths, with its transmission limited primarily on your mirror costing material.

http://www.thorlabs.com/images/TabImages/Concave_metallic_mirror_8_degree_AOI.gif

Any telescope with refractive (transparent glass) elements however, will quickly lose performance outside of the visual range due to transmission, but also from how the glass index changes with wavelength, which causes non-visual light to be defocused (an effect which increases the further you get from visual wavelengths).

Generally speaking, the defocused issue of refractive telescopes can be compensated if you have enough focus travel. You will see "chromatic aberration" becoming much more significant very quickly, as telescopes are only designed to correct this over visual wavelengths.

Ultimately, the limiting factor of refractive telescopes is the transmission of the glass in the lenses. Many glasses will transmit reasonably well from 400-2000nm, though some have worse performance and some have better.