Mission Visa application
A Mission Visa needs to be applied for at the UAE Ministry of Labour (MOL), not the immigration department / DNRD / FNRD (which is presumably why you won't find it on the DNRD website list of visas).
Mission Visa infomormation valid prior to new visa rules introduced in July 2008. Out of date but left here for reference and comparison with other undated information.
The Mission Visa was introduced late 2007 / early 2008 and intended for people working in the UAE temporarily with the permission of the Labour Ministry. The DNRD website information is not very clear - this information comes from articles in the press.
Visa is issued for 3 months, cost is 600 dhs. Extension for another 3 months costs 1200 dhs. Maximum stay is 180 days (so if you stay 6 months, you may be in trouble for the extra couple of days although there is apparently a grace period of 7 days for 3 month visas - may not apply for the second 3 months).
Apparently you need to get a Temporary Work Permit from the Ministry of Labour first before applying for the Mission Visa. MOL website does not have further information about a TWP (at least, not in English).
According to the Interior Ministry, it is only available to expatriate doctors, engineers, lawyers and technicians.
29 September 2007 - New 6 month Mission Visa (superseded by new rules July 2008)
The Ministry of Labour is apparently planning to introduce a new visa, the Mission Visa, valid for residency and employment up to six months. Cost of the Mission Visa is expected to be 1200 dhs. This sounds similar to an already existing Mission Visa, but with no restrictions on job categories. It may be possible to change a Mission Visa to a normal Employment Visa. Information from report in Emirates Today 28 Sep 2007 about the new Mission Visa