Thanks everybody for your answers.
A observation:
I just tried to hook a pressure transmitter up to a small system, and I noticed that when I held my hand around (just around, not bending, shaking or anything else) and heated the small plastic tube, the absolute pressure rose from 50mmWG to 54mmWG.
That is a pretty visual demonstration of one of the error sources a pitot system can have. A small temperature change in only one of the pressure tubes (static and stagnation) result in a massive error – massive compared to a transmitter accuracy of 1% of 20mmWG.
I guess that I prefer hotwire now

Unless, of course, someone can see an error in my observation.
Well, back to the questions:
Assuming that this is for flow in some sort of pipe or duct, what are its dimensions and how much straight run is exists both before and after the measurement section?
The dimensions are not given yet, but the setup should be used for different sizes of ducts.
The straight run has a length of about 50-100cm, depending on the device. The flow exits into a plenum.
If the conduit is relatively large, how is the flow distributed across the measurement section? How stable is the flow rate and distribution across the measurement section?
How the flow is distributed across the section I do not know. The duct may be as small as 5cm and as large as 30cm. Ideally the distribution is uniform, but due to wall gradients in the small duct and upstream anisentropy in general the flow may the skew. But hopefully it is not.
The flowrate should be stable.
What is the purpose of measuring the velocity? Are you looking to measure the flow in a relatively large duct but means of a velocity traverse pattern?
I am looking for differences in flowrate across the duct. And I will traverse the probe across the duct.
Btw, if anyone got links to manufactures of hot-wire equipment (other than the one already given), please share.