Four inches seems alittle high to me,I mow at 3 1/2" and it works great for me. Funny,I just posted how mowing high is the best thing I did this year.

To an extent the more grass blade you leave after mowing the more sunlight that grass blade can utilize and the more nutrients that grass blade can manufacture and send to the plant roots which will send out more grass blades which will thicken your turf. Yes, sometimes with some grass species, the grass blades can "lay" down making mowing a really nice even turf somewhat difficult. I cure that by cross mowing, mowing that spot in a different direction, 90 or 180 degrees from the first time.
Grass blades that turn yellow, while still attached to the root are telling you there is problem that needs to be looked at.

What kind of grass are we talking about? The newer Elite Kentucky bluegrasses can stand to be mowed at 3.5 inches, but otherwise, the turf grasses seem to be more dense at the higher height. I'm thinking you might have a fescue turf that is thinning. Still though, that describes the grass at the hotel I stay at and their grass stands up tall.

Have you had a soil test recently? I never ask that question because I usually have another suggestion, but this seems odd. Also when did you fertilize last? And what is your watering program (when it isn't raining?

sounds like poa trivialis (roughstalk bluegrass). likes moist areas, lays down and often looks dead during the summer, only to come back in the fall. light green color.

"the grass has a tendency to "lay down" and sprout up from the ends"
sounds like the creeping bent grass I have mixed in my lawn,
I try to ignore it,
I consider slit seeding / overseeding KBG,
but understand the bent is tenacious,
did I say ignore it ?

To answer some of your follow up questions-

I haven't watered yet this year. My soil is very high in clay content and with all the rain we have been having this spring in Maryland, the soil has stayed wet/ moist consistently.

My last "fertilizer" application was to spread some alfalfa pellets late last fall after a year of consitent cracked corn and corn meal applications. Earlier this spring I did apply corn gluten meal as a pre-emergent, but I think it also did quite a fertilizer job as the grass has been growing very fast between mowings.

Since I first posted my message, I have collected the grass clippings after mowing and not let them mulch back into the ground. I have a feeling that with all the rain the clippings were breaking down and pushing some of the grass down which was leading to my problem. The only problem area do seem to be where there is a different turf besides tall fescue though. I will look up the roughstalk bluegrass and greeping bent grass- thanks.

What kind of mower are you using? How often do you cut?

Most likely you have clay soil not a "soil with a high clay content". Most every where I was in Maryland had clay soil except a few coastal areas with sand. Grasses do not root from the tips of blades, although the tips may get stuck under some other grass if it is allowed to grow too long. If when mulch mowing grass clippings are left on or near the surface either the person mowing is not cutting often enough or is mowing too fast. When mulch mowing your speed must be that which allows the lawn mower to do the job, and since manufacturers simply do not make good mulching mowers we have to make do and the compromise is not the best.
Contrary to popular opinion law mowing is not a competitive sport and may need to be done more than once a week, depending on how the grass is growing. In the spring grass does grow.

neilc has a good point. I had to go back and reread the original post. If the grass is sending out runners that sprout, that is how the grass spreads. By raking those up, you are keeping the grass from becoming more dense. It could be that your soil is too moist right now for the runners to sprout but I agree with neilc, leave it alone.

Actually, if it is the Bent,
http://www.american-lawns.com/grasses/bentgrass.html
for some, it becomes a weed consideration due to the its matting, spreading nature when cut high.
Since I've transitioned from a short Locke cut, 1 3/4 - 2', to a 3 - 5 ' Scag cut, the low nature of the Bent has presented the chariteristics bhartz describes, patches will rake up like grub damage, but it is just reaching outwards instead of standing and getting cut.
This I try to ignore, bothers my wife more than it does me.
My lawn is a mutt, and I cut the old dog no matter what.

Here is a link that might be useful: http://www.american-lawns.com/grasses/bentgrass.html

Kimmsr- I think you may have hit the nail on the head. Although we have had some drying out since that time, it was raining so often that I wasn't able to cut more than once a week. When I was cutting the grass blades were longer than usual and probably not mulching up as well.

A question for all of you nice enough to respond to my intial query- is it better to cut the grass while it is still wet to keep on schedule or wait until it is dry to cut when it may be too long?

Whenever it is possible, cut it when it is dry.