If the unit has a filter that would be the first place I would check. These are usually at the rear of the unit, and are plainly visable. The next place i would check is just after the inlet solinoid. This is right where the water line enters the unit. Pull the line off of the unit side of the solinoid, and have someone activate the lever. If the flow is low replace the solinoid assembly. After that you will be getting into some serious disassembly of the unit to check the lines for any crush points, There may be a pinch at the dispensor itself, but this is unlikely. A visual inspection with a flashlight up under the dispensor will reveal this.
Solinoids do in fact get weak over time. They are also prone to getting pieces of calcium build up in them.
Yes, they are availavble for purchase at most appliance centers.
Flushing out a solinoid won't do you much good. The problem is most likely going to be a weak solinoid or just plain worn out. If this were a 12 or 24 volt solinoid they have been said to "revive" for a while if hit with a short charge of approximatly 10 to 15 volts higher than they are rated. But this is only a temporary fix and it will soon fail anyways.
As for telling you anything you didnt already know. There are only so many things that can go wrong with one of these systems, and I do not know what you do, or do not know unless you tell me.
I have been told that I am a good expert, but a terrible clairvoyant. lol