Personally I'd go with a 19" CGA monitor and ArcadeVGA card for it. You can buy both and still be out less that the price of the U3100.
Now my bias has been established:

Here are my questions:
1. Sizing. I am planning on using a cabinet kit from Scott @ arcadedepot. Someone posted
that a 19" arcade monitor has an actual viewable image of 19". I am surprised by this
because this means that the tube itself must be larger, like a 20" tube. Can someone
confirm this? Aren't tubes all measured the same? If I end up going with a PC monitor do I
need to look for a really strange 20" model? Did these ever exist?
I don't have a arcade monitor handy to measure (my games are at my shop) but I'm pretty sure the tube is actually 19 inches.
Computer monitors don't project as close to the edge of the tube as either arcade monitors or televisions do. Plus there a marketing angle where "bigger is better" so they use the tube size in big letters and then give you the actual viewable area in the small print.

I'd tend to think the U3100 has a 19" tube, but with such a big dot pitch it probably uses more of the tube face than a normal computer monitor. Either way I wouldn't worry about it, the difference in display area will be minor.
2. Mounting. Does anyone know of a good way to mount a PC monitor. What if it doesn't
have the internal metal cage? Is this much more dangerous than an open frame arcade monitor
because it was never designed to be used outside its case? Do open frame arcade monitors
have more protection from frying yourself (I'm not saying total protection..., just better?)
With a normal PC monitor or TV you're probably better off leaving it in the plastic case. Mounting it will be a matter of bracing it in place so it can't fall to the bottom of the cabinet. Look through the main site for examples of how to do this, there should be several that'll give you an idea of what's involved.
If you're going to mount it vertically, remove the back case half, and drill holes in the sides (which will end up being top and bottom once it's mounted) to allow airflow through the case in that orientation. I'd wait to do this till you have the bracing figured out, there's no point in drilling the case in places where the holes will be covered up.

The protection (when it works) is an arcade cabinet will shut down the monitor when you open the cabinet's backdoor. That and arcade technicians usually know what not to touch on an powered up open frame monitor. Either one is more than capable of shocking your arse across the room.

3. The U3100 has a dot pitch of 0.71. Will this look good for *most* mame games? I know
they say it supports 640x480 and 800x600, but if you do the math there are only about 540
triads across it. I would think this really wouldn't look very good for 640x480 let alone
800x600.
It should look okay for normal raster games, but I tend to think it'd look awful on vector games or in windows. Unless you favor the vector games or plan to web surf from you cabinet I don't think it'd be much of an issue.
4. The U3100 is available with two tube types - ORION vs RCA? What is different or better
about the RCA ?
5. I have heard some say that an arcade monitor doesn't support more than 256 colors. It
seems to me that this is a feature of the video card and not the monitor. Any comments on
this?
I don't know about number 4.
Standard arcade monitors are essentially televisions without a tuner section or case. The inputs are analog, so the color variations don't have limitations like a digital computer monitor.
6. Does the U3100 have scanlines? Are they close to the orignal? How are they different?
Thanks for the help and advice, I really appreciate it.
A VGA monitor has twice as many scanlines as a CGA monitor as it's a function of the horizontal refresh rate. MAME has a scanlines option to fake the look of CGA scanlines, but I can't say how authentic it would look on a U3100. Using them looks better on my 19" desktop monitor, but (IMHO) it's still not quite right compared to playing on a real arcade monitor.
HTH,
Butch...